A Currently with Hill Engineering, LLC

Advanced Tank Car Collaborative Research Program

Research Report

Final Technical Report for Project TWP-10 – Revision 1

Correlating Material Properties to 

Puncture Resistance to Enhance the 

Safety and Security of Tank Cars

 Steven W Kirkpatrick, Ph.D.

Applied Research Associates, Inc.

 Peter C McKeighanA, Ph.D., P.E.

For Exponent – Failure Analysis Associates

March 2018

Sponsored by the industry partners of the 

Advanced Tank Car Collaborative Research Program (ATCCRP):

American Chemistry Council

Association of American Railroads

The Chlorine Institute

The Fertilizer Institute

Railway Supply Institute

 

 
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DISCLAIMER

This report was sponsored by the industry partners of the Advanced Tank Car 

Collaborative Research Program. It is disseminated for informational purposes 

only and is given to, and is accepted by, the recipient at the recipient’s sole risk. 

American Chemistry Council (ACC), Association of American Railroads (AAR), 

The Chlorine Institute (TCI), The Fertilizer Institute (TFI) and Railway Supply 

Institute (RSI) make no representation or warranties, either expressed or implied, 

with respect to this report or its contents. ACC, AAR, TCI, TFI and RSI assume 

no liability to anyone for special, collateral, exemplary, indirect, incidental, 

consequential, or any other kind of damages resulting from the use or application 

of this report or its contents. Any attempt to apply the information contained in this 

report is made at the recipient’s own risk.
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Table of Contents

Section Page

Acknowledgements........................................................................................................................ ix

Abstract .......................................................................................................................................... x

1 Introduction and Background ................................................................................................. 1

1.1 Problem Definition and Approach.................................................................................. 1

2 Material Constitutive and Damage Models ............................................................................ 3

2.1 Introduction..................................................................................................................... 3

2.2 Material Stress-Strain Behavior...................................................................................... 3

2.2.1 Background Information on Continuum Mechanics................................................... 3

2.2.2 The Von Mises Yield Criterion................................................................................... 8

2.2.3 The Drucker Prager Yield Criterion ........................................................................... 9

2.3 Material Damage Models.............................................................................................. 10

2.3.1 Bao-Wierzbicki Failure Surface ............................................................................... 10

2.3.2 Modified Bao-Wierzbicki Failure Criterion ............................................................. 13

2.3.3 Maximum Strain Failure Criterion............................................................................ 14

2.3.4 Gurson-Tvergaard Failure Criterion ......................................................................... 23

2.4 Data Reduction Procedures for Material Characterization Test Data........................... 24

3 Material Characterization Testing and Analyses.................................................................. 32

3.1 Testing Overview.......................................................................................................... 32

3.1.1 Material..................................................................................................................... 33

3.1.2 Pre-Test Material Characterization........................................................................... 34

3.1.3 Test Matrices and Experimental Methods ................................................................ 39

3.2 Overview of Results...................................................................................................... 44

3.2.1 Smooth Specimen Tensile Properties ....................................................................... 46

3.2.2 Notched Specimen Tensile Properties...................................................................... 54

3.2.3 Shear Properties........................................................................................................ 56

3.3 Model Calibration for the Alternative Materials Characterized ................................... 57

3.3.1 NUCU Material Properties ....................................................................................... 58

3.3.2 HPS100W Material Properties.................................................................................. 60

3.3.3 A514B Material Properties....................................................................................... 62
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3.4 Evaluation of TC128B Steel samples........................................................................... 64

3.4.1 NGRTC TC128B Material Properties ...................................................................... 65

3.4.2 ATCCRP TC128B Material Properties .................................................................... 73

3.5 Evaluation of Puncture Resistance for Alternative Tank Car Materials....................... 81

3.5.1 Tank Car Puncture Modeling.................................................................................... 83

3.6 Tank Car Puncture Modeling........................................................................................ 88

3.6.1 Description of Different Stress-Strain Curve Parameters......................................... 88

3.6.2 Influence of Stress-Strain Parameters on Puncture Force......................................... 90

3.7 Puncture Energy Models............................................................................................... 98

3.7.1 Model Form and Calibration..................................................................................... 98

3.7.2 Model Sensitivity to Input Stress-Strain Parameters.............................................. 102

3.7.3 Applying the Puncture Models to Different Materials ........................................... 103

4 Summary and Conclusions ................................................................................................. 107

5 References........................................................................................................................... 110

Appendix A – Supplemental Data .............................................................................................. 114

Appendix B – Characterization of 304L Stainless Steel............................................................. 115

Introduction ............................................................................................................................. 115

Characterization Testing.......................................................................................................... 115

Summary and Conclusions...................................................................................................... 124
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List of Figures

Figure Page

Figure 1. Local damage criterion for tensile ductile fracture analyses........................................ 11

Figure 2. Bao-Wierzbicki failure surface and tests used for model calibration........................... 12

Figure 3. Bao-Wierzbicki failure surface and tests used for model calibration........................... 13

Figure 4. Comparison of the Bao-Wierzbicki and maximum strain failure criteria. ................... 15

Figure 5. Comparison of the tensile test analyses with different failure criteria. ........................ 16

Figure 6. Comparison of notched round bar tensile tests with different failure criteria.............. 18

Figure 7. Comparison of the tensile-shear test analyses with different failure criteria. .............. 19

Figure 8. Comparison of tank car puncture analyses with different failure criteria. ................... 20

Figure 9. Calculated stress triaxiality in the impact zone for a 6x6-inch side impact. ................ 20

Figure 10. Calculated stress triaxiality in the impact zone for a coupler side impact. ................ 21

Figure 11. Calculated stress triaxiality in the impact zone for a 6x6-inch offset head impact.... 21

Figure 12. Calculated tank head impact damage with the Bao-Wierzbicki failure criterion....... 22

Figure 13. Calculated tank head impact damage with the maximum strain failure criterion. ..... 22

Figure 14. Comparison of the Gurson-Tvergaard, Bao-Wierzbicki, and 

maximum strain failure criteria. ................................................................................ 23

Figure 15. Material testing data for different TC128B materials. ............................................... 24

Figure 16. Comparison of engineering and true stress-strain data for TC128B. ......................... 26

Figure 17. Tabular true stress curve developed for the TC128B constitutive model. ................. 27

Figure 18. Comparison of the measured and calculated TC128B tensile test. ............................ 27

Figure 19. Comparison of Tensile test data and analysis for 0.777-in-thick TC128B 

using a von Mises yield criterion. ............................................................................. 29

Figure 20. Comparison of notched tensile tests and analysis for 0.777-in-thick TC128B 

using a von Mises yield criterion. ............................................................................. 29

Figure 21. Calculated stress-strain paths for the notched tensile tests on 

0.777-in-thick TC128B. ............................................................................................ 30

Figure 22. Comparison of Tensile test data and analysis for 0.777-in-thick TC128B 

using aDrucker-Prager yield criterion. ...................................................................... 31

Figure 23. Comparison of notched tensile tests and analysis using a 

Drucker-Prager yield criterion................................................................................... 31

Figure 24. Microstructure of the three Phase II TC128B materials............................................. 36

Figure 25. CVN fracture toughness as a function of temperature for Phase II

TC128B materials...................................................................................................... 39
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Figure 26. Three different notched tensile specimen geometries with a 2-inch gage length....... 42

Figure 27. Shear test specimen utilized for testing...................................................................... 43

Figure 28. Different test setups for (a) smooth, (b) notched, and (c) shear tests......................... 44

Figure 29. Characterization test data for the ATCCRP NUCU Steel.......................................... 45

Figure 30. Characterization test data for the ATCCRP HPS100W Steel. ................................... 45

Figure 31. Characterization test data for the ATCCRP A514B Steel.......................................... 46

Figure 32. Tensile property comparison of Phase I non-TC128B materials. .............................. 47

Figure 33. Tensile property comparison of Phase I and II TC128B materials. ........................... 48

Figure 34. Notch strength comparison of Phase I non-TC128B materials.................................. 55

Figure 35. Notch strength comparison of Phase I and II TC1288B materials............................. 55

Figure 36. Notch ductility ratio comparison of Phase II TC128B materials. .............................. 56

Figure 37. Shear strength comparison of Phase II TC128B materials......................................... 57

Figure 38. Comparison of tensile test stress-strain behaviors for the Phase I materials.............. 58

Figure 39. Model calibration for the ATCCRP NUCU Steel. ..................................................... 60

Figure 40. Model calibration for the ATCCRP HPS100W Steel. ............................................... 62

Figure 41. Model Calibration for the ATCCRP A514B Steel..................................................... 64

Figure 42. Comparison of tensile stress-strain curves from various TC128B samples............... 65

Figure 43. Comparison of tank car puncture analyses with different failure criteria. ................. 66

Figure 44. Characterization test data for the NGRTC Tank Car 3069 TC128B plate................. 66

Figure 45. Model calibration for the NGRTC Tank Car 3069 TC128B plate............................. 68

Figure 46. Characterization test data for the NGRTC Tank Car 3074 TC128B plate................. 69

Figure 47. Model calibration for the NGRTC Tank Car 3074 TC128B plate............................. 69

Figure 48. Characterization test data for the NGRTC new normalized 

0.777-inch TC128B plate. ......................................................................................... 71

Figure 49. Model calibration for the NGRTC new normalized 0.777-inch TC128B plate......... 73

Figure 50. Characterization test data for the baseline ATCCRP 0.750-inch TC128B plate. ...... 74

Figure 51. Model calibration for the baseline ATCCRP 0.750-inch TC128B plate.................... 74

Figure 52. Characterization test data for the baseline ATCCRP Arcelor Medium Sulfur 

TC128B plate. ........................................................................................................... 76

Figure 53. Model calibration for the Arcelor Medium Sulfur TC128B plate.............................. 76

Figure 54. Characterization test data for the baseline ATCCRP SSAB Low Sulfur 

TC128B plate. ........................................................................................................... 78

Figure 55. Model calibration for the SSAB Low Sulfur TC128B plate. ..................................... 78
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Figure 56. Characterization test data for the baseline ATCCRP Trinity Low Sulfur 

TC128B plate. ........................................................................................................... 80

Figure 57. Model calibration for the Trinity Low Sulfur TC128B plate..................................... 80

Figure 58. Candidate tank car steels with a range of mechanical properties............................... 82

Figure 59. Tank model and impact zone mesh used for side impact puncture analyses. ............ 83

Figure 60. Detailed impact and puncture sequence for a 600 lb chlorine car.............................. 84

Figure 61. Calculated puncture initiation and fracture progression............................................. 84

Figure 62. Calculated puncture forces for candidate tank car steels............................................ 86

Figure 63. Calculated puncture energies for candidate tank car steels........................................ 86

Figure 64. Relative puncture force performance for candidate tank car steels............................ 87

Figure 65. Relative puncture energy performance for candidate tank car steels......................... 87

Figure 66. Relative puncture protection performance for candidate tank car steels.................... 88

Figure 67. Definition of the characterization of a material’s stress-strain behavior.................... 89

Figure 68. Comparison of the TC128B and HY-80 material tensile stress-strain curves............ 91

Figure 69. Relative puncture force after ultimate stress correction............................................. 92

Figure 70. Relative puncture force after yield stress correction .................................................. 94

Figure 71. Calculated force deflection curve for various material tanks..................................... 94

Figure 72. Calculated force deflection curve for various materials with 

yield stress corrections. ............................................................................................. 95

Figure 73. Relative puncture force after two different corrections including ductility. .............. 97

Figure 74. Curve fit comparisons and results for the three different models 

(data shown used to derive curve fit parameters).................................................... 100

Figure 75. Model results for different variants of TC128B and other materials. ...................... 105
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List of Tables

Table Page

Table 1. Tabular TC128B stress-strain curve values................................................................... 28

Table 2. Material donated by Union Tank Car for the Phase I evaluations 

(rolling direction parallel to the short, 8-inch, dimension of the plates). .................. 33

Table 3. TC128B material donated by various sources for the Phase II evaluations. ................. 34

Table 4. Chemical composition of the three non-TC128B materials. ......................................... 35

Table 5. Chemical composition of the Phase I and Phase II (A-, S- and T-) 

TC128B materials...................................................................................................... 37

Table 6. Hardness and room temperature CVN tests for the three non-TC128B materials. ....... 37

Table 7. Hardness and room temperature CVN tests for the four different 

TC128B materials...................................................................................................... 38

Table 8. Test matrix for each material involved in the material property testing (Phase I). ....... 40

Table 9. Test parameters for the smooth and notched tensile tests at quasistatic rate (Phase I).. 40

Table 10. Test parameters for the variable rate tensile tests (Phase I)......................................... 41

Table 11. Test matrix for each material involved in the material property testing (Phase II)..... 41

Table 12. Measured tensile properties for both orientations (Phase I). ....................................... 49

Table 13. Notched tensile test results (L-orientation, Phase I).................................................... 50

Table 14. Quasistatic and high rate tensile test results (L-orientation, Phase I).......................... 51

Table 15. Measured tensile properties for the three TC128B variants in Phase II. ..................... 52

Table 16. Notched tensile results (L orientation) for the three TC128B variants in Phase II. .... 53

Table 17. Shear test results for the three TC128B variants in Phase II. ...................................... 54

Table 18. Material constitutive parameters and tabular NUCU stress-strain values................... 59

Table 19. Material constitutive parameters and tabular HPS100W stress-strain values ............. 61

Table 20. Material constitutive parameters and tabular A514B stress-strain values................... 63

Table 21. Material constitutive parameters and tabular stress-strain values 

for the Tank Car 3069 TC128B................................................................................. 67

Table 22. Material constitutive parameters and tabular stress-strain values 

for the Tank Car 3074 TC128B................................................................................. 70

Table 23. Material constitutive parameters and tabular stress-strain values 

for the new normalized 0.777-inch TC128B............................................................. 72

Table 24. Material constitutive parameters and tabular stress-strain values 

for the ATCCRP 0.750-inch TC128B....................................................................... 75
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Table 25. Material constitutive parameters and tabular stress-strain values

for the Arcelor Medium Sulfur TC128B................................................................... 77

Table 26. Material constitutive parameters and tabular stress-strain values 

for the SSAB Low Sulfur TC128B ........................................................................... 79

Table 27. Material constitutive parameters and tabular stress-strain values 

for the Trinity Low Sulfur TC128B .......................................................................... 81

Table 28. Baseline normalized puncture force scaled with different stress-strain parameters.... 92

Table 29. Curve fit parameters for the two different models....................................................... 99

Table 30. Curve fit results for the three different models.......................................................... 101

Table 31. Puncture energy change resulting from different stress-strain parameter changes. .. 103

Table 32. Predicted puncture energy for different variants of TC128B and other materials..... 104
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Revision History

Rev. Date Sections Description

0 Feb. 2018 All Original report sponsored and released by the Advanced Tank Car 

Collaborative Research Program (ATCCRP).

1 Mar. 2018 Appendix B

Minor editorial corrections to the body of the report

Appendix B added to describe the work performed under ATCCRP 

TWP-10A to characterize ASTM A240 Type 304L stainless steel and 

develop a corresponding constitutive model.
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Acknowledgements

This program would not have been possible without the support of a number of organizations. 

First, the guidance of the Advanced Tank Car Collaborative Research Program (ATCCRP) group 

in assisting in this effort was invaluable and insightful during this work. Organizations that 

donated material for this effort are hereby recognized: Union Tank Car, Arcelor Mittal, SSAB 

and Trinity Industries. Several subcontractors performed testing on this program included 

Metcut (Cincinnati, OH) and University of Dayton Research Institute (Dayton, OH). Arcelor 

Mittal supported this effort and performed much of the initial characterization work for this 

program. Finally, numerous fruitful discussions were held with A.D. McKisic (Trinity), William 

Heitmann (Arcelor Mittal), Tanya Ros (Arcelor Mittal), Carl Hybinette (formerly Union Tank 

Car) and Phil Daum (ESI). Finally the support and patience of the Association of American 

Railroads during execution of this project is acknowledged.

This report describes analyses performed for the ATCCRP under a contract with the Association 

of American Railroads (AAR). Additional ATCCRP industry partners supporting this effort 

include the American Chemistry Council (ACC); the Chlorine Institute (CI); The Fertilizer 

Institute (TFI); and the Railway Supply Institute (RSI). The analysis methodologies used in this 

report build on the work previously performed under the Next Generation Rail Tank Car 

(NGRTC) Project.
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Abstract

In the Next Generation Railroad Tank Car Project, testing and analysis were performed on 

TC128B material as well as other tank car steels (e.g. A1011, A516-70). In a similar material 

evaluation effort, the Chlorine Institute sponsored a program to characterize other high strength 

low alloy (HSLA) candidate steel materials (A710, HPS 70, and HPS 100). In this study, this 

past data is used and augmented by additional testing and analysis to evaluate the impact and 

puncture resistance performance of candidate materials that could be used in tank car structure 

(both shell and jacket). Understanding the appropriate form of material damage and failure 

models, predicting structural performance and linking behavior to basic material properties, will 

allow design optimization and selection of the most appropriate material for the tank structures.

The research program included detailed characterizations of various steel material samples 

(including a number of different TC128B variants). These detailed material characterizations 

included assessing tensile stress-strain properties as well as mechanical behavior of notched 

samples. As part of the research, detailed constitutive and damage models were developed for 

each material and the models were used to simulate the corresponding tests. 

An unexpected result of this process was that the commonly used von Mises yield criterion could 

not adequately model the full range of tests in the material characterization data. Specifically, 

the von Mises assumption that the yield condition is independent of the mean stress resulted in 

the inability of the model to reproduce the load displacement curves for both the smooth and 

notched tensile tests. Moreover, as originally conceived, a number of different material failure 

models were proposed including the Bao-Wierzbicki, Gurson-Tvergaard and a maximum strain 

approach. In the end, the only suitable model for the materials considered herein was found to 

be the Bao-Wierzbicki model.

In addition to the direct material characterization, a series of puncture analyses were performed 

for various candidate materials to identify the material characteristics that most strongly control 

puncture resistance. Candidate materials with a wide range of mechanical properties were used 

in a suite of puncture analyses under various side impact conditions using a chlorine tank car 

geometry. These puncture results were then correlated to basic material properties (strength and 

ductility) with the form of the empirical correlations being simple linear combinations of 

different strength and ductility terms. Although these models are empirical, the roles of yield 

strength, ultimate strength, and ductility (percent elongation) are apparent from this modeling in 

terms of controlling puncture behavior.

The resulting correlations provide a predictive tool to rapidly screen candidate materials and 

hence avoid expensive and time-consuming laboratory tests and full-scale simulations on 

materials that will not yield significant performance improvements. Applying these models 
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(correlations) to various combinations of strength and ductility indicates that most common

materials will net at best a modest improvements in puncture performance when compared with 

incumbent materials. The models indicate that significant improvements in puncture 

performance require candidate materials with markedly higher strength and ductility 

combinations than the incumbent materials (e.g. TC128B). 
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Correlating Material Properties to Puncture Resistance 

to Enhance the Safety and Security of Tank Cars

1 Introduction and Background

There is ongoing research to develop strategies for improving railroad tank cars so they can 

maintain tank integrity for more severe accident conditions than current equipment. Research 

results are being used to develop improved tank car designs and inform rulemaking by the 

Pipeline and Hazardous Materials Safety Administration (PHMSA). One area of research is to 

evaluate the effects of different steel materials that can be applied for enhanced tank car puncture 

protection. This report describes research to characterize and evaluate the performance of 

different steels. 

A significant portion of the previous tank car material characterization testing and constitutive 

modeling methodologies were developed under the Next Generation Railroad Tank Car 

(NGRTC) Program [1]. A key effort in the NGRTC Program was the development and 

validation of detailed finite element constitutive and failure models which can be used to 

accurately predict the puncture resistance under different impact conditions. These validated 

methodologies are being applied in this study to assess the puncture protection potential of 

various candidate tank car steels. 

In the Next Generation Tank Car Project analysis and testing was performed on TC128B 

material as well as other tank car steels (e.g. A1011, A516-70) [2-8]. In a similar material 

evaluation effort, the Chlorine Institute sponsored a program to characterize other high strength 

low alloy (HSLA) candidate steel materials (A710, HPS 70 and HPS 100) [9]. In this study, this 

past data is used and augmented by additional testing and analysis to evaluate the performance of

these and other candidate materials that could be used in tank car structure (both shell and 

jacket). Understanding the appropriate form of material damage and failure models, predicting 

structural performance and linking behavior to basic material properties, will allow design 

optimization and selection of the most appropriate material for the tank structure.

The research described in this report extends these previous material characterization and 

modeling efforts and was performed as part of the Advanced Tank Car Collaborative Research 

Program (ATCCRP). The analysis methodologies used in this report build on the work of the 

previous research. 

1.1 Problem Definition and Approach

Accident statistics show that the rail industry’s safety performance has generally improved over 

the last few decades. The Federal railroad Administration’s (FRA) Railroad Accident and 

Incident Reporting System (RAIRS) show that the number of accidents per year with at least one
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car releasing hazardous materials has decreased significantly over the past 25 years [10]. 

However, a series of three clustered accidents or derailments involving the release of hazardous 

material focused attention on the structural integrity of railroad pressure tank cars. These events 

included (1) Minot, ND, on January 18, 2002; (2) Macdona, TX, on June 28, 2004; and (3) 

Graniteville, SC, on January 6, 2005 [11-13]. More recently, the July 6, 2013 derailment and fire 

of the crude oil tank car train in Lac-Mégantic, Quebec, along with other oil train derailments, 

have expanded the interest in improved puncture resistance for general purpose tank cars. 

There are several proposed methods to improve the puncture resistance of tank cars. The most 

common are (1) increased thickness of the tank and/or jacket, (2) top and bottom fittings 

protection, (3) improved tank car materials, and (4) advanced protection systems such as 

sandwich structures or composites. Of these, the approach using improved tank car steels has the 

advantages of both maintaining the existing tank car designs and manufacturing processes and 

obtaining improved puncture resistance without adding weight to the tank car.

The approach in the study had three primary tasks. The first was to review and collect past work 

related to tank car and other candidate steels. This included the testing and analysis already 

completed by the NGRTC research program as well as other studies and structural applications. 

In addition, the Tank Car Committee efforts to identify and evaluate candidate TC128B 

replacement materials were included. 

The second task in this study was to evaluate different analysis methodologies and material and 

damage models suitable for tank car puncture analyses. While substantial puncture modeling 

work has already been performed by Applied Research Associates, Inc. (ARA) and Quest 

Reliability, it is necessary to re-visit these analyses, review them critically, and assess where they 

work or do not work. Three primary failure criteria were considered: the Bao-Wierzbicki (BW), 

the Gurson-Tvergaard (G-T), and the critical plastic strain models. 

The final task in this program was material characterization testing. It was anticipated that much 

of this study would use existing test data minimizing the need to generate additional 

experimental data. However, testing was required for new candidate steel materials that provide 

enhanced protection. In addition, additional testing was required on conventional tank car 

materials to address variability and metallurgical composition effects. 
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2 Material Constitutive and Damage Models

2.1 Introduction

Tank car impact and puncture analyses require a model for the material constitutive and damage 

behaviors to accurately predict the puncture threshold under various impact conditions. A 

piecewise linear elastic-plastic constitutive model was modified for this purpose to include the 

Bao-Wierzbicki (BW) failure criterion [14-16]. This model has been applied by other 

researchers to assess tank car puncture conditions [17] and is capable of reproducing both the 

nonlinear stress-strain behavior of the material as it deforms into the plastic regime and the 

fracture and failure behavior that depends on the state of stress and plastic strain history in the 

material. The material parameters used in these constitutive models were developed from the 

material test data on TC128B steel, developed under the NGRTC program [2-8]. 

The following sections describe the development of the constitutive and damage parameters used 

in the subsequent tank car puncture analyses. 

2.2 Material Stress-Strain Behavior

2.2.1 Background Information on Continuum Mechanics

At the onset of this project, it was assumed that we would be applying typical computational 

methodologies for metal plasticity. These include a material model that applies a von Mises 

yield criterion and a hardening law based on the effective plastic strain. Although these 

modeling methodologies are appropriate for most applications of analysis of steel structures, we 

found that a fundamental assumption for these models was not suitable for the very detailed 

assessment of the material behaviors in different stress conditions. In particular, the von Mises 

criterion assumes that the yield stress is independent of the hydrostatic stress that resulted from 

experimental observations on metal plasticity, notably by Bridgeman [18]. We found in this 

study that the von Mises criterion could not reproduce the full range of material behaviors 

measured for the materials with sufficient accuracy. 

Because we extended our investigation to include more advanced constitutive theories, we 

thought it helpful to include some background information on continuum mechanics. The 

information provided here uses descriptions from various sources including a background paper 

on effective stress and effective plastic strain [19] and other reference on continuum mechanics 

[e.g. 20]. 

The development of constitutive relations to describe nonlinear material response has a rich 

history drawing on developments in both experimental and theoretical mechanics. As a class of 

materials, metals have received the most attention from experimentalists and theoreticians in 
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developing constitutive relations which describe their behavior over a wide range of 

environments and applications. Many of the basic ideas and a lot of the terminology used to 

describe the behavior of other materials have their origin in the development of constitutive 

relations for metals. It is within the context of metal plasticity that the definition and function of 

effective stress and effective plastic strain will be presented. 

2.2.1.1 Invariants of the Stress Tensor, σσiiii·

The stress tensor is assumed to be symmetric (σij = σji) and has six independent components 

which are defined at a point with respect to a set of coordinate axes. There are three normal 

stresses, σxx, σyy, and σzz, and three shear stresses, σxy, σyz, and σzx. It is always possible to select 

a special set of axes through the point so that the shear stress components are zero in the special 

coordinate system. These special axes are called principal axes and the three non-zero stress 

components are called principal stresses, which will be denoted as σ1, σ2, and σ3.

The principal stresses are physical qualities, scalar numbers, whose values do not depend on the 

coordinate system in which the components of stress were initially given. They are therefore 

invariants of the stress state, invariant with respect to rotation of the coordinate axes to which the 

stresses are referred. Similarly, the symbols Iσ, IIσ, and IIσ in the following scalar expressions 

denote additional invariants of the stress tensor with respect to rotation of the reference axes:

I σ = σσxxxx + σσyyyy + σσzzzz = σii

IIσ = σσxxxxσσyyyy + σσyyyyσσzzzz + σσzzzzσσxxxx − σσxx

2 − σσyy2 − σσzz2 = 1

2

(σiiσjj-σijσij) (1)

IIIσ = = σσxxxxσσyyyyσσzzzz − σσxxxxσσyy

2 − σσyyyyσσzz2 − σσzzzzσσxx2 + 2σσxx σσyy σσzz

If the axes of reference are chosen to align with the principal axes of the stress tensor, the much 

simpler algebraic forms given below are found in terms of the principal stresses.

I σ = σσ1 + σσ2 + σσ3

IIσ = σσ1σσ2 + σσ2σσ3 + σσ3σσ1 (2)

IIIσ = = σσ1σσ2σσ3

In any two coordinate systems, the numerical value of any of the individual components will in 

general be different, but the numerical value of the invariants will be the same. 
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I σ is called the first invariant of the stress tensor; it is also called the trace of the stress matrix, 

denoted tr(σσ), which is the sum of the elements of the main diagonal (the three normal stresses). 

The second invariant II σ is a homogeneous quadratic expression in the stress components; it is 

the sum of the three minor determinants of the diagonal elements in the determinant of the stress 

matrix. The third invariant III σ is the determinant of the stress matrix, denoted by det(σσ), and is 

a homogeneous cubic expression in the stress components. These tensor invariants should be 

thought of as characterizing a tensor, just as the length invariant characterizes to some extent a 

vector. Many writers use the notation I 1, I 2, I 3 or J 1, J 2, J 3 instead of I σ, II σ, III σ for the 

invariants of the stress tensor.

2.2.1.2 Spherical and Deviatoric Stress Tensors·

The stress tensor, σij, can be written as the sum of two tensors, one representing a spherical or 

hydrostatic state of stress and the second called the deviatoric stress (SSiiii). Let σσ� denote the 

mean normal stress (p is the mean normal pressure). 

σσ� = −pp = 1

3 � σσxxxx + σσyyyy + σσzzzz� = 13

σii (3)

Thus for the deviatoric stress we have

SSiiii = σσiiii − σσ�δδiiii (4)

where δδiiii is the Kronecker delta defined by

δδiiii = �

1 if i = j

0 if i ≠ j (5)

Many writers use the notation σσiiii

′ instead of Sii for the deviatoric stress.

In general, the deviatoric stress is associated with changes in shape, while the hydrostatic stress 

produces volume change without changing the shape in an isotropic continuum, i.e. in a material 

with the same properties in all directions.

2.2.1.3 Invariants of the Deviatoric Stress Tensor, SSiiii·

The principal directions of the deviatoric stress tensor are the same as those of the stress tensor, 

since both represent directions perpendicular to planes having no shear stress. Although the 

principal directions are the same for the deviatoric and stress tensors, the principal values are not 

the same. The principal deviator stresses are the principal stresses scaled by subtracting the mean 

normal stress (adding the pressure) and are given by
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SSkk = σσkk − σσ� = σσkk + pp (6)

In the same manner that we found the invariants of the stress tensor, we may also determine the 

invariants of the deviator stress. The invariants of the deviatoric stress tensor are given by

IS = SS1 + SS2 + SS3= 0

IIS = SS1SS2 + SS2SS3 + SS3SS1 (7)

IIIS = = SS1SS2SS3

which are analogous to those given for the stress tensor by Eqs. (2), but calculated with the 

principal components of the deviatoric stress. Note that the first invariant of the deviatoric 

stress, IS, is zero since we defined the deviatoric stress to be the stress tensor minus the pressure. 

Alternative expressions for IIS are

IIS = 1

2

SSiiiiSSiiii= 

1

2 ( SSxxxx

2 + SSxxxx2 + SSxxxx2 ) + σσxx2 + σσyy2 + σσzz2 (8)

IIS = 

1

6 � � σσxxxx − σσyyyy�

2

+ � σσyyyy − σσzzzz�

2

+ ( σσzzzz − σσxxxx)2� + σσxx

2 + σσyy2 + σσzz2 (9)

IIS = 

1

6 [ ( σσ1 − σσ2)2 + ( σσ2 − σσ3)2 + ( σσ3 − σσ1)2] (10)

Some writers use the notation J1, J2, and J3 to denote the invariants of the deviatoric stress tensor, 

but the most common notation is JJ2

′

and JJ3

′ which we will use in the following discussion of 

constitutive relations; since JJ1

′ = 0, it is seldom used.

2.2.1.4 Generalized Yield Criteria

A yield criterion determines what levels and combinations of three dimensional stress states 

permit inelastic (plastic) response to begin. This can be expressed mathematically as

ff�σσiiii� < 0 ffffff eeeeeeeeee ee rr

ff�σσiiii� = 0 ffffff pp rr

(11)

This yield condition can be interpreted geometrically in terms of a surface ff�σσiiii� = 0, i.e. a 

hypersurface in a nine-dimensional space in which the stresses σσiiii are interpreted as nine 

Cartesian coordinates. Since σσiiii is symmetric, we can alternatively interpret the yield surface as a 
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surface in six-dimensions. If the stress state is inside the surface, ff�σσiiii� < 0, the response is 

elastic. If the stress state is on the surface, ff�σσiiii� = 0, the response is plastic. Note that the 

stress state is never outside of the surface; ff�σσiiii� ≤ 0 always. If the stress state is estimated to 

lie outside the yield surface, then the surface moves (kinematic hardening) or changes shape 

(isotropic hardening) and/or the strains are adjusted (plastic straining) until ff�σσiiii� = 0.

We now consider additional assumptions, limiting the generality of the yield criteria and some 

consequences that follow from the assumptions. Not all the additional assumptions are made in 

every plasticity theory, but all are included in the theories most widely used for metal plasticity.

2.2.1.5 Assumption 1. Yield is independent of the spherical part of the stress.

Experimental observations by Bridgeman [18], indicate that plastic deformation of metals is 

essentially independent of hydrostatic pressure. Because of the difficulties in loading a specimen 

in hydrostatic tension, most experimental verifications have been limited to superimposed 

hydrostatic compression, but the postulate is also assumed to apply to hydrostatic tension. It 

follows from this assumption that the function ff�σσiiii� must in fact be a function only of the 

deviatoric stress.

ff�σσiiii� = ff�SSiiii� (12)

2.2.1.6 Assumption 2. The material is isotropic.

If the material is isotropic, there can be no preferred direction and the yield function should have 

the same form for all orientations of the rectangular Cartesian coordinate axes relative to the 

material. This implies that the yield function should only depend on the principal values of the 

stress and indeed it must be a symmetric function of the principal values of stress, since an 

isotropic material is unable to distinguish one principal direction, and associated principal value, 

from another.

One way to mathematically express this symmetry condition of the yield function is to use the 

invariants of the stress rather than the principal values. This is possible since the invariants are 

completely determined by the principal values and are symmetric functions of the principal 

values. The reader may easily verify that the stress invariants given in Eqs. (6) are symmetric 

functions of the principal values.

Assumptions 1, f is independent of pressure thus f = f�Sij�, and 2, f is symmetric and thus f =

f(Iσσ,IIσσ,IIIσσ), imply that f must be a function of the invariants of the deviatoric stress tensor. 

Thus the yield function must be expressible as
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ff�σσiiii� = ff( JJ2

′, JJ3′ ) (13)

for an isotropic material which is independent of the hydrostatic part of the stress tensor.

2.2.1.7 Assumption 3. Yield is independent of the sign of the stresses.

For most isotropic polycrystalline metals the initial yielding in tension and compression occurs at 

the same level of stress. This is usually postulated to apply to the general yield function by 

requiring

ff�−σσiiii� = ff�σσiiii� (14)

This assumption and the assumption of isotropy may both lead to significant departures from 

observed behavior when applied to materials after previous plastic deformation, but experience 

indicates that they work reasonably well for initial yield. In frictional materials, such as soil, 

rock, or concrete, Assumption 3 is definitely incorrect, since these materials are much weaker in 

tension than compression, e.g. these materials fracture, crack, or pull apart in tension.

2.2.2 The Von Mises Yield Criterion

The two simplest, and most widely used yield criteria are the Tresca criterion and the von Mises

criterion. Both of these criteria satisfy all three of the above assumptions about the form of yield 

criteria functions. We will concern ourselves only with the von Mises criterion, since its use is 

much more prevalent in numerical analyses, while the Tresca criterion is more often used in 

closed form analyses due to its less complex form for simple states of stress.

von Mises suggested that yielding occurs when the second invariant of the deviatoric stress JJ2

′

reaches a critical value, or

�JJ2

′ = kk (15)

in which kk is a material parameter to be determined. This yield criterion mayalso be written as

σσee = �3JJ2

′ = √3kk (16)

and σσeeeeee is termed the effective stress, generalized stress, or equivalent stress. 

Some physical insight into the definition of effective stress is gained by considering the case of 

uniaxial yielding. For the uniaxial case the principal stresses at yield are σσ1 = σσyy, σσ2 = σσ3 = 0

and thus
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−pp = 1

3 ( σσ1 + σσ2 + σσ3) = 13

σy (17)

and

SS1 = σσ1 + p == 2

3

σy

SS2 = σσ2 + p = − 1

3

σy (18)

SS3 = σσ3 + p = − 1

3

σy

then

JJ2

′ = 1

2

SSiiiiSSiiii= 

1

2 ( SS1

2 + SS22 + SS32) = 1

3σσyy

2 = kk2 (19)

Or for the von Mises criterion

σσee = σσyy = �3JJ2

′ (20)

2.2.3 The Drucker Prager Yield Criterion

As described in the previous section, one of the primary assumptions built into the von Mises

yield model is that the yield is independent of the spherical part of the stress. However, this 

approximation was challenged in the 1970s by the experiments of Richmond, Spitzig, and Sober 

[21-24]. They studied the effects of hydrostatic pressure on the yield strength of various steels. 

Their research found that the yield was dependent on the hydrostatic stress level at pressure 

levels significantly less than the maximum pressures used by Bridgman years earlier.

In general, the independence of yield on hydrostatic stress is a reasonable approximation for 

analysis of ductile metals. However, some researchers have determined the need to eliminate 

this approximation for analysis of specific metals and loading conditions [e.g. 25-26]. The most 

common approach in this case is to apply a yield function identical to one proposed by Drucker 

and Prager [27] for soils described the yielding process. The Drucker-Prager yield function can 

be written as a modification of the von Mises yield criterion [19, 20] that includes a term 

dependent on the first stress invariant as:

�JJ2

′ + ααIσσ = kk (21)

This form of yield function is included in later analyses of the materials tested in this program.
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2.3 Material Damage Models

Accurate prediction of the response and puncture behavior of tank car materials requires a 

nonlinear constitutive and damage model. The primary function of the constitutive model is to 

determine the internal forces (stress) that are developed as the material is deformed (strained) 

under various loading and deformation conditions. The corresponding damage model 

determined the accumulation of damage and corresponding failure of the material for a given 

deformation history. 

The damage models described here apply local fracture mechanics approaches (LFM) that model

the microstructural deformation and failure processes leading to fracture in terms of continuum 

parameters averaged over a small volume of material [28-35]. LFM focuses on the evolution of 

the process zone, in contrast to classical linear elastic and elastic-plastic fracture mechanics 

(LEFM and EPFM, respectively), which characterize fracture in terms of the boundary 

conditions of the fracture process zone. Although LFM may initially seem more complex to 

formulate and more difficult to apply than LEFM/EPFM, it is more versatile and more general. 

LFM is also ideally suited to implementation into finite element analyses where damage can be 

evaluated at the local element level. 

One objective of the analyses in this study was to evaluate a few commonly used damage models 

for ductile materials. The most commonly used failure criterion is to apply a single critical value 

of the plastic strain. The damage model applied for puncture analyses in the NGRTC program

[1] was the Bao-Wierzbicki (BW) model. An alternate failure model applied in a series of 

analyses for the Chlorine Institute was the Gurson-Tvergaard (G-T) model [9]. These models are 

described in the following sections.

2.3.1 Bao-Wierzbicki Failure Surface

The key mechanism that needs to be included in the ductile local fracture model for tank car 

puncture analyses is the influence of the stress state on the rate of damage development as the 

material is undergoing plastic deformation. The primary stress state factor that controls the rate 

of damage development is the stress triaxiality, defined as the ratio of the mean stress to the 

equivalent stress (σmean/σeq). The mean stress (or hydrostatic stress) and equivalent stress (or

effective stress or the von Mises stress) were defined previously in Equations (15) and (16). 

There are many models that include the effects of stress triaxiality on damage development and 

ductility. Several of these have previously been applied within LS-DYNA to analyze various 

ductile fracture problems [e.g. 36-38] including the use of the Gurson-Tvergaard model [39-41] 

for the puncture assessment of pressure tank cars [42]. These models have the ability to include 

the stress triaxiality effects on ductility for tensile loading as illustrated in Figure 1. The 

deficiency with many of these previous local damage models is that they do not include the 
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changes in damage development and failure for low triaxiality where the tensile damage and 

failure behavior transitions into a shear dominated fracture behavior. The concern that shear 

fracture behavior is important for tank car puncture assessment led to the selection of the BaoWierzbicki (BW) model in this effort.

Figure 1. Local damage criterion for tensile ductile fracture analyses.

As implemented, the BW model is a basic form of a ductile fracture criterion [31]. It assumes 

that failure at a material location occurs when the damage within a surrounding characteristic 

volume (VMIC) exceeds a critical value. The damage development and failure criterion can be 

written in the form

( ) ∫ = = 1

c mean eq

p

eq d

D

ε σ σ

ε

over VMIC (22)

where D is the normalized damage parameter; p d eq ε is an increment in equivalent plastic strain; 

and ( ) c σ mean σ eq ε is the critical failure strain as a function of the stress triaxiality. The 

characteristic volume (VMIC) in this application is the element size which was maintained with a 

characteristic element length of approximately 0.040 inch (1 mm) in the fracture zone. Damage 

accumulation occurs with plastic deformations and the damage is tracked locally in each element 

in the model. When the damage level in any element exceeds the failure criterion (D=1), the 

local failure is propagated in the model by element erosion.
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The critical strain function is that proposed in the BW criterion and contains multiple branches 

depending on the range of stress state as shown in Figure 2. The critical strain in each branch are 

governed by the equation

( )

( )

( ) ( )

[( )] ( )

( ) ( ) 





















≤

− + ≤ ≤

− ≤ ≤

+

∞ ≤ −

=

mean eq

mean eq

mean eq mean eq

mean eq

mean eq

mean eq

c mean eq

B

B A A

A

σ σ

σ σ

σ σ σ σ

σ σ

σ σ

σ σ

ε σ σ

3

1

3

3

1 9( ) 0

0

3

1

1 3

3

1

2

(23)

And the parameters A and B can be determined by a series of tests under different stress 

conditions including notched tensile tests with specimens of varying notch radii [43] and tensileshear tests with different ratios of tension to shear stress. 

Figure 2. Bao-Wierzbicki failure surface and tests used for model calibration.
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2.3.2 Modified Bao-Wierzbicki Failure Criterion 

The Bao-Wierzbicki criterion was found to provide a good fit to the failure data for many of the 

materials tested. However, for some materials, the model as applied could not fit the failure data 

over the range of triaxialities tested. An example is seen in the data from three different TC128B 

materials tested in the NGRTC program as shown in Figure 3. The BW model provides a 

reasonably good fit to the data for both the Normalized 0.777 and Tank Car 3074 materials (Red 

and green curves and data points). However, the Tank Car 3069 material is the most ductile in 

the smooth round bar tensile tests (triaxiality = 0.33-0.60) and least ductile at the sharpest 

notched tensile test (triaxiality ≅ 1.4). 

Figure 3. Bao-Wierzbicki failure surface and tests used for model calibration.

There are different approaches that can be used to obtain a better fit to the data. In the original 

work of Bao and Wierzbicki they allow the point at which the local maximum ductility is 

reached, set at the uniaxial stress triaxiality ratio of 1/3 in this study, to be a variable that is 

adjusted in the model. Alternatively, other ductile damage models have different functional 

forms for the decay in ductility at higher stress triaxialities. 

In this study, we used a modified functional form for the high triaxiality branch of the damage 

function. This was accomplished by adding an exponent (n) to the denominator to the equation 

for the critical strains at high triaxiality. This modified BW damage model is provided in 

Equation 24. 
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( )

( )

( ) ( )

[( )] ( )

[ ( )] ( ) 





















≤

− + ≤ ≤

− ≤ ≤

+

∞ ≤ −

=

n mean eq

mean eq

mean eq mean eq

mean eq

mean eq

mean eq

c mean eq

B

B A A

A

σ σ

σ σ

σ σ σ σ

σ σ

σ σ

σ σ

ε σ σ

3

1

3

3

1 9( ) 0

0

3

1

1 3

3

1

2

(24)

2.3.3 Maximum Strain Failure Criterion

In this section, we explore an alternate damage modeling methodology which is called the

maximum strain or critical plastic strain criterion. This is the most commonly used failure 

criterion applied in engineering failure analyses. This simple approach is typically applied using 

a critical strain value from a single source (e.g. tensile test) to determine the critical plastic strain 

value. The advantage of the maximum strain approach is both the ease of use and common 

availability in many constitutive models of most nonlinear finite element codes. Like most 

damage models, the maximum strain methodology has computational issues, such as mesh 

sensitivity, which can complicate analyses and need to be controlled. 

A comparison of the Bao-Wierzbicki and maximum strain failure criteria are shown in Figure 4. 

The maximum strain failure criterion uses a constant value of plastic strain for failure for all 

stress states. As a result, we would expect the maximum strain failure criterion to be more 

ductile than the BW criterion in some loading conditions (e.g. high triaxiality notched tensile 

tests and shear tests) and less ductile in other loading conditions (e.g. compression). 

To evaluate the Maximum Strain Approach (MSA), the maximum strain criterion was used to 

simulate the TC128B material tests from the NGRTC program using the existing FE models. 

The results were compared to the results to the test data and BW model simulations to assess the 

performance of the MSA model for tank car puncture applications. 

The methodology that was applied is:

1. Recover archived NGRTC models of the laboratory material tests for the tensile, notched 

tensile, tensile-shear, and punch tests on the TC128B material. 

2. Convert the BW constitutive model used in the NGRTC program for TC128B to be a model 

controlled by a maximum strain failure criterion.

3. Calibrate the critical maximum strain value to match the data on the tensile tests. 
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4. Use the calibrated value to assess the failure modeling performance in the high-triaxiality 

(Notched tensile: 3 configurations)) and low-triaxiality (tensile-shear: 7 configurations) 

stress regime tests. Similarly the punch shear tests (3 configurations) will be analyzed and 

compared to analyses with the BW model. 

5. Document the comparisons of the BW and MSA approach for the laboratory tests and 

identify areas where discrepancies occur. 

The two constitutive models being applied in this assessment are identical up to the point of 

failure. The only difference in the two approaches is in the criterion used to determine the point 

at which the material fails. 

Figure 4. Comparison of the Bao-Wierzbicki and maximum strain failure criteria.

Simulations of the smooth round bar tensile test with the BW and maximum strain criteria are

compared to the measured tensile response in Figure 5. Overall there is good agreement between 

the calculated and measured stress-strain behavior and elongation at failure with both models. 

However, this is expected since the critical plastic strain value (plastic strain of 1.0) was selected 

to match in this test condition. We see in Figure 4 that the critical strain value is slightly below 

the value in the BW criterion at a uniaxial stress loading condition (triaxiality=0.333). However, 

as the specimen starts to neck the triaxiality increases and the critical BW- strain value in the 

necked region would drop below maximum strain value. Thus the average value in the 

simulation for the BW model is close to the critical plastic strain value. 
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(a) Bao-Wierzbicki failure model

(b) Maximum strain failure model

Figure 5. Comparison of the tensile test analyses with different failure criteria.
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Simulations of the notched round bar tensile test with the BW and maximum strain criteria are 

compared to the measured tensile response in Figure 6. There is good agreement between the 

calculated and measured stress-strain behavior and elongation at failure with the BW model, 

shown in Figure 6(a). However, the analyses with the maximum strain criterion significantly 

overpredict the ductility of the notched tensile tests compared to the measured behavior. This is 

not surprising since the critical plastic strain value (plastic strain of 1.0) is significantly above 

that of the BW criterion for the high triaxiality states of these notched tests (triaxiality values of 

0.7-1.4). 

Similar simulations of the tensile-shear tests with the BW and maximum strain criteria are 

compared to the measured tensile response in Figure 7. Again, there is good agreement between 

the calculated and measured stress-strain behavior and elongation at failure with the BW model, 

shown in Figure 7(a). However, the analyses with the maximum strain criterion significantly 

overpredict the ductility of the tensile-shear tests compared to the measured behavior. This is not 

surprising since the critical plastic strain value (plastic strain of 1.0) is above that of the BW

criterion for the low triaxiality states of the shear tests (triaxiality values of 0.0-0.3). 

The above comparisons of the maximum strain criterion clearly indicate that there are some 

loading conditions where the MSA does not accurately predict the failure of the material. 

However, there are also applications where the simpler maximum strain criterion is sufficiently 

accurate. The final comparison of the two failure criteria is for the blunt side impact puncture 

respose of tanks. When we compare the analyses of tank puncture performance using the BW

and maximum strain failure criteria we get very similar behaviors, as shown in Figure 8. The 

puncture forces are quite similar with slightly higher forces calculated for the BW failure 

criterion for the smaller impactors. The puncture energies are also similar with the exception of 

the 6x6 impactor where a slight increase in the puncture force allowed some late time tank 

kinematics to be included and this increases the calculated puncture energy by approximately 

30% for this case. However, this result is specific to the details of the impact kinematics and 

would not be typical for most other scenarios (e.g. different impact speed). Note that for the 

impact behaviors analyzed, the strain rates are relatively low and strain rate effects were not 

included in the models. This approach is consiustent with the previous tank car puncture 

analysis programs [e.g. 1]. 

A closer inspection of the impact calculations explains why the two failure criteria are in 

reasonable agreement for the tank puncture analyses. The failure typically initiates on the inside 

surface of the tank under the impact zone where the metal is deformed in tension. At these 

locations, the stress triaxiality is typically in the range between 0.5 and 0.7 for a variety of 

impactors and tank impact scenarios as shown in Figure 9 through Figure 11. 
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(a) Bao-Wierzbicki failure model

(b) Maximum strain failure model

Figure 6. Comparison of notched round bar tensile tests with different failure criteria.
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(a) Bao-Wierzbicki failure model

(b) Maximum strain failure model

Figure 7. Comparison of the tensile-shear test analyses with different failure criteria.
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Figure 8. Comparison of tank car puncture analyses with different failure criteria.

Figure 9. Calculated stress triaxiality in the impact zone for a 6x6-inch side impact.
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Figure 10. Calculated stress triaxiality in the impact zone for a coupler side impact.

Figure 11. Calculated stress triaxiality in the impact zone for a 6x6-inch offset head impact.

Although the prediction of the tank punctures occurs at similar levels with the BW and critical 

strain criteria, the comparison of analyses show an important difference. The predicted damage 

in the impact zone for the 6x6 offset head impact with the BW and critical strain failure criteria 

are shown in Figure 12, and Figure 13, respectively. The BW model predicts that the failure 

initiates on the inside surface of the tank (dominated by tensile deformations). In contrast, the 
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maximum strain criterion predicts that the failure initiates on the outer surface of the tank in a 

region dominated by compressive stress states during deformation. 

Figure 12. Calculated tank head impact damage with the Bao-Wierzbicki failure criterion.

Figure 13. Calculated tank head impact damage with the maximum strain failure criterion.
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2.3.4 Gurson-Tvergaard Failure Criterion

The damage model applied for puncture analyses in the NGRTC program was the BaoWierzbicki (BW) model. An alternate failure model applied in a series of analyses for the 

Chlorine Institute was the Gurson-Tvergaard (GT) model [9]. An illustration of the GT failure 

criterion compared to the BW failure criterion is shown in Figure 14. The model has the 

characteristic of capturing the reduction in ductility for the high triaxiality stress conditions. As 

applied in Reference 9, the emphasis of the material evaluations was on the high triaxiality 

material ductility. In that study, various materials were characterized by, and the material 

models were fit to, Charpy impact test results. 

Figure 14. Comparison of the Gurson-Tvergaard, Bao-Wierzbicki, and maximum strain failure 

criteria.

Since the completion of that effort, two different aspects of this approach have been 

reconsidered. The first is that the assumption that the entire damage curve scales with the 

ductility in the Charpy impact test may not be accurate. The models that are fit to the variability 

in the Charpy energy may not be appropriate to assess the difference in puncture behavior. This 

is the effect that required development of the Modified Bao-Wierzbicki damage model described 

in Section 2.3.2. The variability in Charpy impact test ductility is not proportional to the 

ductility in tensile behaviors. 

The second aspect of the G-T model is that researchers have identified that it does not accurately 

capture the ductility of a model for low stress triaxiality levels [e.g. 44-47]. As a result, the G-T 

model was not further examined in this study. 
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2.4 Data Reduction Procedures for Material Characterization Test Data 

A tabular stress-strain curve was developed based on testing of different samples of TC128B [1, 

2]. A series of standard tensile tests were performed on different batches of TC128B, as shown 

in Figure 15. The data is consistent within each batch of material but significant variation can be 

found in tank car material obtained from different sources. The new material that was tested was 

at the upper range of strength for TC128B and the material recovered from the tank cars used in 

the test were more consistent with previous test data [48, 49]. As a result, the material recovered 

from the tank car used as the Test 2 target vehicle was used as the baseline material for the 

analyses in this report. 

Figure 15. Material testing data for different TC128B materials.

The data shown in Figure 15 is the measured engineering stress-strain behavior. Engineering 

stress was obtained by dividing the measured loads by the original cross-sectional area of the 

specimen. Similarly, engineering strain was obtained by dividing the change in the specimen 

gauge-section length by the original length. 

The constitutive model in the finite element analyses requires that the engineering data be 

converted to a true stress and true strain. This conversion accounts for the changing cross 

section of the specimen as it was deformed. The specimen cross section changes (shrinks) 

significantly during the test, and the engineering stress does not yield the “true” stress in this 

cross section. Similarly, the engineering strain is not representative of the material behavior, 

especially when a general three-dimensional state of strain exists. As a result, the engineering 
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stress decreases as some materials approach failure, implying a weakening of the material. In 

reality, the stress in the cross section is increasing due to the reduction in the cross-sectional area 

(i.e. necking).

There are several different ways to measure stress and strain based on the coordinate system used 

[20]. Some are based on material (Lagrangian) coordinates and some on spatial (Eulerian) 

coordinates. These give rise to terms such as “Green” and “Almansi” strain tensors. These are 

important in writing a computer code to solve large strain problems. An alternate approach is to 

define a “true” or “natural” stress and strain. The true stress is based on the load divided by the 

actual cross-sectional area of the specimen and is equal to the engineering stress multiplied by a 

term to correct for the change in cross section.

(1 e) σ T = σ eng + (25)

where σ T and σ eng are the true and engineering stresses, respectively, and e is the engineering 

strain.

Prior to the onset of localization (necking), the natural or true strain, T ε , is defined as

ln( ) ln(1 e) l

l

o

ε T = = + (26)

This definition comes about from defining the incremental true or “natural” strain as the current 

“change in length” divided by the current length, or

l

dl dε T = (27)

This is in contrast with the definition of engineering strain that references the change in length, 

∆l , divided by the original length, 0l , or

0l

l

e

∆ = (28)

After the onset of localization, the determination of the true strain in the necked region becomes 

more complex and requires measurement of the local neck geometry.

The TC128B engineering test results are compared to the converted true stress and true strain 

data in Figure 16. The true stress curves from the tests do not include a correction for the 

necking behavior. As a result, they are only valid up to the onset of necking at a true strain of 

approximately 15%. The actual true-stress and true strain curves for the material continue to 

strain harden throughout the loading if the effects of necking were corrected. An extrapolated 
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true stress curve that corrects for the effects of the necking behavior is added to Figure 16 (solid 

black line). It is this extrapolated curve that is used in the material constitutive model. 

Figure 16. Comparison of engineering and true stress-strain data for TC128B.

The final step in obtaining the tabular stress-strain parameters for the TC128B constitutive model 

was to fit a smooth set of points to the extrapolated true-stress data. This final tabular fit for the 

TC128B is shown in the true stress versus plastic strain curve in Figure 17. The specific values 

for the tabular stress-strain curve are also listed in Table 1. As a validation that this curve 

accurately captures the true stress-strain behavior of the material, a tensile specimen model was 

generated and the constitutive parameters were applied to simulate the tensile test response. The 

calculation was analyzed to determine the engineering stress-strain behavior consistent to the 

tests (e.g. using equivalent gauge section length). A plot of the calculated engineering behavior 

compared to the test data is shown in Figure 18. The data shows that the constitutive parameters 

accurately reproduce the material behaviors including the onset and development of necking in 

the specimen. 
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Figure 17. Tabular true stress curve developed for the TC128B constitutive model.

Figure 18. Comparison of the measured and calculated TC128B tensile test.
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Table 1. Tabular TC128B stress-strain curve values

Point No. Plastic Strain (in/in) True Stress (ksi)

1 0.00e+00 58.0

2 8.22e-04 54.6

3 1.30e-02 54.8

4 2.76e-02 66.5

5 5.41e-02 79.5

6 9.87e-02 90.2

7 1.49e-01 96.0

8 1.15e+00 165.0

The above procedure is that used for fitting the true-stress-true strain behavior for a model using 

the von Mises yield criterion. The Drucker Prager model requires use of additional data at 

different levels of stress triaxiality (e.g. notched tensile data). Consider the data reduction of the 

0.777-inch-thick normalized TC128B material from the NGRTC Program [1]. An initial data 

reduction was applied using the von Mises model methodology described above and a 

comparison of the tensile test data to the simulation of the tensile test is shown in Figure 19. The 

overall agreement for the tensile test behavior is good. However, when we use the same model 

with the von Mises yield criterion to simulate the notched tensile tests we get the correlation 

shown in Figure 20. The model with the von Mises yield criterion significantly over predicts the 

measured test loads, especially for the sharper notch radii. 

The error in the calculated versus measured load levels for the sharper notch tensile tests, 

combined with knowledge of the triaxiality levels in the various tests, can be used to calculate an 

estimate of the Drucker Prager coefficient (αα in Equation 21, Section 2.2.3). The stress 

triaxiality versus plastic strain paths for the various tensile tests are shown by the dashed lines in 

Figure 21. The uniaxial tensile test starts with a triaxiality of 0.33 and the triaxiality increases as 

the specimen starts to neck (localized in the failure zone) to a maximum value of approximately 

0.5. By comparison, the sharpest notched tensile test has an average triaxiality of approximately 

1.4. Thus the notch results in a much larger tensile mean stress in the specimen gauge section. 
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Figure 19. Comparison of Tensile test data and analysis for 0.777-in-thick TC128B using a von 

Mises yield criterion.

Figure 20. Comparison of notched tensile tests and analysis for 0.777-in-thick TC128B using a 

von Mises yield criterion.
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Figure 21. Calculated stress-strain paths for the notched tensile tests on 0.777-in-thick TC128B.

After the Drucker Prager coefficient has been determined, the true-stress true-strain curve used in 

the constitutive model needs to be corrected to match the uniaxial tensile data. At times, some 

additional adjustment is needed to ensure the model correctly predicts the behavior through 

necking. However, when the parameters have been correctly determined, the model can predict 

the behaviors significantly better over the range of stress states in the tests. 

A comparison of the measured and calculated tensile test results for the normalized 0.777-in 

TC128B material using the Drucker Prager yield function (α=0.195) is shown in Figure 22 and 

Figure 23. The comparisons show good agreement for all levels of confinement (strength and 

ductility). 
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Figure 22. Comparison of Tensile test data and analysis for 0.777-in-thick TC128B using a 

Drucker-Prager yield criterion.

Figure 23. Comparison of notched tensile tests and analysis using a Drucker-Prager yield 

criterion.
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3 Material Characterization Testing and Analyses

3.1 Testing Overview

The first step in the development of a constitutive model is the development of the nonlinear 

stress strain behavior. This governs the mechanical response of the material and prescribes the 

internal forces (stress) that are developed as the material is deformed (strained). 

The purpose of this section is to provide a complete description of the materials testing 

performed and the methods employed. Testing was performed on seven different steel material 

lots during two distinct testing phases. Of the seven materials, four were nominally TC128B 

with three other different steel alloys. The initial first Phase I focused on a typical TC128B and 

the other three medium strength steels. During the second Phase II testing, the focus was on 

TC128B with lower levels of sulfur in the composition of the material (nominal TC128B limits 

sulfur concentration to 0.015% by weight). The testing performed in the two phases was similar, 

although high rate tensile tests in Phase I were replaced with notched shear tests in Phase II.

Sulfur is not a deliberate addition into TC128B material; rather it occurs at differing levels 

depending upon the cleanliness of the material, the source of the melt and the methods used 

during compositional refinement. The role of sulfur in TC128B is evident from Heitmann et al1

who reports significant improvements in transverse CVN (Charpy v-notch) fracture toughness at 

lower and upper shelf temperatures with low sulfur concentrations (<0.006%). It is anecdotally 

reported that the modern steelmaking process has resulted in significant improvements in alloy 

cleanliness, with decreased sulfur concentrations resulting as a benefit of this.

A recent report2 clearly illustrates high sulfur concentrations are apparent in older rail tank cars. 

As part of this report, TC128B composition was examined in 28 retired tank cars built between 

1965 and 1999, with 80% of these fabricated prior to 1980. The reported sulfur weight percent 

values for TC128B were 67% with sulfur <0.03% (only 14% of the total with ≤0.01%) and 33% 

with sulfur ≥0.03%. Clearly the vast majority of these levels exceed the typical sulfur weight 

percent of ≤0.01% produced in modern steels today.

 1 Heitmann, W.E., Feher, F.C., Hybinette, C. and Manohar, M., “The Influence of Sulfur Concentration Below 

0.006% Along With Sulfide Shape Control on the Charpy V-Notch Properties of Normalized and Stress Relieved 

TC128 Grade B Steel Plate,”STEEL: 4th International Symposium on Railroad Tank Cars, Sept. 2007, Detroit MI, 

Materials Science and Technology (MS&T) 2007.

2 McKeighan, P.C., “Mechanical Properties of Tank Car Steels Retired from the Fleet,” Southwest Research 

Institute Project No. 18.12240, Foster-Miller Subcontract SUB3-00022, DOT Volpe Contract No. 

DDTS.060183.000.801, June 2007. 
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3.1.1 Material

The ideal material for this evaluation would have both a range of strengths as well as upper shelf 

toughnesses. For Phase I, materials for this work were donated by Union Tank Car in 

conjunction with characterizations being performed at Miner Enterprises (Geneva, IL). The 

specific alloys and materials included in this study are detailed in Table 2 and include the 

following:

• TC128B: rail tank car steel (0.75-inch thick),

• A709-Gr. HPS100W: moderate strength bridge steel (1-inch thick),

• NUCU: a higher strength bridge steel, nominally ASTM A710-GrB (0.5-inch thick), and,

• A514-GrB: current higher strength bridge steel (0.75-inch thick).

Table 2. Material donated by Union Tank Car for the Phase I evaluations 

(rolling direction parallel to the short, 8-inch, dimension of the plates).

Material No. of Pieces Size of Piece 

(inch)

Thickness

(inch)

A709-Gr. HPS100W 3 8 x 12 1.0

NUCU steel

(A710-Gr B)

3 8 x 12 0.5

A514-Gr B 2 8 x 12 0.75

TC128B normalized 2 8 x 12 0.75

All of these materials were supplied in the normalized condition. The motivation for the Phase II 

testing was due to increasing interest in the rail tank car community to utilize the improved 

toughness low sulfur steels combined with the fact that the Phase I TC128B material had a high 

level of sulfur present.

Phase II materials included three different TC128B heats donated by SSAB, Arcelor Mittal and 

Trinity Industries. A description of these three heats of TC128B is shown in Table 3 and can be 

summarized as follows:

• TC128B – nominal sulfur content (“A-material”) flat plate,

• TC128B – ultra-low sulfur content (“S-material”) flat plate,

• TC128B – ultra-low sulfur content (“T-material”) curved plate extracted from a tank car 

undergoing fabrication.
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All materials were nominally supplied in the normalized condition, although the Trinity material 

was remnants from tank car production (the cutout from the manway). Hence this plate had been 

formed into one of the rings that make-up the tank car. Due to this deformation, this plate was 

subjected to a post-weld heat treatment (PWHT) prior to testing by Arcelor Mittal during the 

material characterization phase. This PWHT cycle was performed in accordance with AAR M1002, Appendix W, paragraph 16 guidelines. It was heated from room temperature to 1150°F, 

held for 1 hour, and furnace cooled until 800°F when it was subsequently removed and air 

cooled.

Table 3. TC128B material donated by various sources for the Phase II evaluations.

Material

Source

Material

Descriptor

Prefix

Identifier

Size of 

Piece (inch)

Thickness 

(inch) Known Pedigree

Arcelor nominal 

sulfur A-material 12 x 12 0.729 Arcelor heat no. 812A38770

SSAB ultra-low 

sulfur S-material 8 x 12 0.505 SSAB heat no. W2L567

Trinity ultra-low 

sulfur T-material 8 x 11 0.729

Manway cutout subsequently 

PWHT, originally produced by 

Arcelor heat no. 821Y13090

The rolling directions for the different materials were all marked on the plates received.

3.1.2 Pre-Test Material Characterization

Before a more extensive test program ensued, some basic material characterization was 

performed on the seven different heats of steel. This is important to ensure that the plates meet 

specification and exhibit expected behavior prior to embarking on a more extensive testing 

effort. This basic characterization work included alloy elemental composition measurements, 

plate hardness measurements, and room temperature longitudinal and transverse CVN fracture 

toughness.

The chemical compositions of the three non-tank car steels is shown in Table 4 and the TC128B 

heats in Table 5. All test materials exhibited chemical compositions within the specifications of 

the appropriate material. The Phase I TC128B exhibited a sulfur composition of 0.008% (high 

sulfur) whereas Phase II included a medium sulfur (A-material, 0.005%) and two ultra-low sulfur 

heats (S-material and T-material, 0.002% and 0.0025%, respectively). Recall too that the S- and 

T-materials differed in thickness (thinner, 0.5-inch thick S-material as opposed to 0.73-inch Tmaterial). The grain structures of the three Phase II TC128B materials are shown in Figure 24. 
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The grain structure was the typical fine grain microstructure observed in TC128B with banding 

and linear stringer features indicating plate rolling with consistent plate center and near edge 

microstructures (see Figure 24).

The materials listed in Table 5 were procured to assess the role of sulfur. Any other material 

differences or microstructural differences between the materials that could have had an effect on 

properties were not considered in this work (hence beyond the scope of this program). For 

instance, Table 5 indicates that the differences in the four materials are not only sulfur content 

but also other elemental species (as well as potentially processing variables from the different 

material suppliers). For example, the nickel content of the SSAB material is markedly greater 

than any of the other TC128B samples. 

Table 4. Chemical composition of the three non-TC128B materials.

Composition, weight percent

A709 Gr. HPS100W NUCU (A710-Gr. B) A514 Gr. B

Element spec measured spec measured spec measured

Carbon <0.08 0.06 0.03–0.40 0.07 0.12–0.21 0.19

Manganese 0.95–1.5 0.99 0.4–0.8 0.71 0.70–1.00 0.93

Phosphorus <0.015 0.006 <0.035 0.006 <0.035 0.011

Sulfur <0.006 <0.005 <0.04 <0.005 <0.035 <0.005

Silicon 0.15–0.35 0.26 0.4–0.6 0.42 0.20–0.35 0.24

Nickel 0.65–0.90 0.79 0.65–1.0 0.94 n/a 0.21

Chromium 0.40–0.65 0.51 n/a 0.07 0.40–0.65 0.44

Molybdenum 0.40–0.65 0.48 n/a 0.05 0.15–0.25 0.17

Copper 0.9–1.2 1.1 1.3–1.5 1.4 n/a 0.20

Aluminum 0.02–0.05 0.03 n/a 0.03 n/a 0.03

Vanadium 0.04–0.08 0.06 n/a <0.01 0.03–0.08 0.03

Niobium 0.01–0.03 0.02 <0.006 0.004 n/a <0.01

Titanium n/a <0.01 <0.03 0.03 0.01–0.03 0.02

Boron <0.006 <0.005 n/a 0.005 <0.005 0.002

Hardness and room temperature CVN fracture toughness was also evaluated as shown in Table 6

and Table 7. The measured hardness of the materials was consistent with expectation for the 

expected strength levels of the materials:

• HPS100W: expected UTS 110-130 ksi, UTS inferred from hardness 129 ksi

• NUCU: expected UTS >82 ksi, UTS inferred from hardness 98 ksi

• A514B: expected UTS 110-130 ksi, UTS inferred from hardness 124 ksi
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• TC128B: expected UTS 81-101 ksi, UTS inferred from hardness for the four 

heats 84-90 ksi

(a) A-material (medium sulfur)

(b) S-material (low sulfur)

(c) T-material (low sulfur)

Figure 24. Microstructure of the three Phase II TC128B materials.
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Table 5. Chemical composition of the Phase I and Phase II (A-, S- and T-) TC128B materials.

Element

Composition, weight percent

AAR App M Ph. I matl A-matl S-material T-material

spec (2012) measured measured heat measured heat measured

Carbon <0.26 0.23 0.21 0.20 0.19 0.22 0.21

Manganese 1.00 – 1.70 1.39 1.37 1.37 1.39 1.34 1.27

Phosphorus <0.025 0.030 0.008 0.008 0.009 0.014 0.014

Sulfur <0.015 0.008 0.005 0.001 0.002 0.002 0.0025

Silicon 0.15 – 0.50 0.44 0.35 0.20 0.20 0.34 0.33

Nickel no limit 0.02 0.010 0.17 0.170 0.01 0.008

Chromium no limit 0.21 0.16 0.12 0.13 0.16 0.16

Molybdenum no limit 0.07 0.06 0.06 0.06 0.057 0.05

Copper <0.35 0.03 0.020 0.25 0.241 0.016 0.013

Aluminum 0.015 – 0.060 0.03 0.035 0.023 0.022 n/a 0.027

Vanadium <0.084 0.06 0.066 0.043 0.041 0.055 0.050

Niobium n/a <0.01 0.002 0.002 0.003 n/a 0.001

Titanium <0.02 <0.01 0.001 0.001 0.002 0.002 0.003

Boron <0.0005 <0.005 0.0002 0.0001 0.0004 0.0002 0.0001

Nitrogen <0.012 n/a 0.0085 0.0065 0.0067 n/a 0.0070

Tin <0.02 n/a n/a 0.009 n/a n/a n/a

Carbon EQ (CE) <0.55 0.53 0.50 0.50 0.50 0.50 0.48

Cu+Ni+Cr+Mo <0.65 0.33 0.25 0.60 0.60 0.24 0.23

Nb+V+Ti <0.11 0.020 0.003 0.046 n/a n/a 0.064

Ti/N <4.0 n/a 0.12 0.15 0.30 n/a 0.43

CE = %C + %Mn/6 + (%Cr + %Mo + %V)/5 + (%Cu + %Ni)/15

Table 6. Hardness and room temperature CVN tests for the three non-TC128B materials.

Material

Hardness Room Temperature (73°F) CVN energy, ft-lbs

Rockwell B- or C- Longitudinal Transverse

A B C A B C A B C

HPS100W

27 27 26 180 181 191 205 213 201

Rc =27 ∼ 129 ksi UTS TYP ∼ 180 ft-lbs TYP ∼ 205 ft-lbs

NUCU

93 93 94 143 135 139 175 187 175

Rb =93 ∼ 98 ksi UTS TYP ∼ 139 ft-lbs TYP ∼ 175 ft-lbs

A514B

25 25 25 94 96 96 139 143 132

Rc =25 ∼ 124 ksi UTS TYP ∼ 96 ft-lbs TYP ∼ 139 ft-lbs
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Table 7. Hardness and room temperature CVN tests for the four different TC128B materials.

TC128B

Material

Pedigree

Hardness Room Temperature (73°F) CVN energy, ft-lbs

Rockwell B or Brinell (HB) Longitudinal Transverse

A B C A B C A B C

Phase I

87 88 87 70 70 46 53 65 64

Rb =87 equiv to HB 170

(∼84 ksi UTS) TYP ∼ 70 ft-lbs TYP ∼ 65 ft-lbs

A-material

185 185 186 134 124 102 99 107 108

HB = 185 (∼90 ksi UTS) TYP ∼ 120 ft-lbs TYP ∼ 105 ft-lbs

S-material

188 187 180 118 115 119 105 117 133

HB = 185 (∼90 ksi UTS) TYP ∼ 117 ft-lbs TYP ∼ 119 ft-lbs

T-material

175 174 169 132 121 136 148 143 150

HB = 173 (∼86 ksi UTS) TYP ∼ 130 ft-lbs TYP ∼ 147 ft-lbs

As an indication of upper shelf hardness, CVN toughness was evaluated at room temperature 

conditions (even though most materials have specifications for low temperature toughness, this 

particular aspect of the materials was not evaluated during this program). Transverse room 

temperature toughnesses for the non-TC128B materials were in the range of 140-200 ft-lbs 

whereas for TC128B values of 70-150 were evaluated.

Toughness is expected to increase with decreasing sulfur content for TC128B (see, for instance, 

earlier referenced Heitmann paper). An examination of the upper shelf toughness values in 

Table 7 clearly indicates this with the high sulfur Phase I material exhibiting 65 ft-lbs (room 

temperature), the medium sulfur (A-material) at 105 ft-lbs and the two low sulfur materials in the 

range of 120-150 ft-lbs. For the Phase II TC128B’s evaluated in Phase II, additional CVN tests 

were performed as a function of temperature as shown in Figure 25. Although the data is 

scattered, the most pronounced influence of temperature was apparent for the longitudinal 

specimens (bottom plot, Figure 25) with the lowest temperature CVN toughness approximately 2

times greater for the low sulfur conditions. 
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Figure 25. CVN fracture toughness as a function of temperature for Phase II TC128B materials.

3.1.3 Test Matrices and Experimental Methods

The testing performed during Phase I and Phase II are described in detail in Table 8-Table 11. 

All tests were performed under room temperature conditions. All seven materials were subjected 

to the following tests:

• Tensile stress-strain tests on smooth specimens in both the longitudinal and transverse 

orientation

• Tensile stress-strain tests on notched specimens (three notch radii: 0.05, 0.10 and 0.25-

inch) in the longitudinal orientation

Longitudinal

Temperature, °F

-40 -20 0 20 40 60 80 100

CVN Fracture Toughness, ft-lbs

0

25

50

75

100

125

150

Med S (A-matl)

Low S (S-matl)

Low S (T-matl)

Transverse

-40 -20 0 20 40 60 80 100

CVN Fracture Toughness, ft-lbs

0

25

50

75

100

125

150
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• Phase I testing only – tensile stress-strain tests on smooth specimens (reduced gage 

length) in the longitudinal orientation at three different rates: quasistatic, intermediate and 

high loading rate.

• Phase II testing only – shear tests on a 0.5-inch thick specimen with a notch radius of 

0.05-inch.

Table 8. Test matrix for each material involved in the material property testing (Phase I).

Specimen

Geometry

Gage

Length

Notch

Radius Test Rate SpecimenOrientation

No. of

Replicates

smooth 2-inch none

quasistatic L 2

quasistatic T 2

smooth 0.75-inch none

quasistatic L 2

intermediate L 2

highest possible L 2

notched 2-inch

0.25-inch quasistatic L 2

0.10-inch quasistatic L 2

0.05-inch quasistatic L 2

Table 9. Test parameters for the smooth and notched tensile tests at quasistatic rate (Phase I).

Quantity Smooth Notched

Gage dimensions (inch): 0.25D x 2.0 0.25D net, various notches

Test specification: ASTM E8-11 none (spirit of E8)

Extensometer gage length (inch): 1.0 0.5

Head rate <5% ε (inch/minute): 0.005 0.030

Head rate >5% ε (inch/minute): 0.050 0.030

Test temperature: RT RT
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Table 10. Test parameters for the variable rate tensile tests (Phase I).

Quantity Smooth

Gage dimensions (inch): 0.25D x 0.75

Test specification: ASTM E8-11

Extensometer gage length (inch): 0.5

Open Loop Head Rate (inch/second):

Intermediate Head Rate (inch/minute):

1.4 – 1.6

0.02

Open Loop Strain Rate (inch/inch/second)

Intermediate Strain Rate (inch/inch/minute):

0.50 – 0.55

0.01

Test temperature: RT

Table 11. Test matrix for each material involved in the material property testing (Phase II).

Specimen

Geometry

Overall

Dimensions

Notch

Radius Test Rate SpecimenOrientation

No. of

Replicates

smooth 2-inch GL none

quasistatic L 2 – 4

quasistatic T 2 – 4

notched 2-inch GL

0.25-inch quasistatic L 2 – 3

0.10-inch quasistatic L 2

0.05-inch quasistatic L 2

shear 0.5” thick 0.05-inch quasistatic L 2 – 3

The change in testing between Phase I and Phase II was due to ongoing modification of program 

goals and objectives based upon results from analyses performed during the program. 

Tensile and notch testing was performed in accordance with the ASTM E8 metallic material 

tensile test standard. For the smooth tensile testing, ASTM standard 2-inch and 0.75-inch gage 

length specimens were utilized. The notched specimen design shown in Figure 26, with different 

sized notches and a fixed net section diameter, is based upon testing performed during the 

previous NGRTC program. The shear test specimen utilized during testing, Figure 27, was also 

adopted from the previous NGRTC testing program. Note that this shear test evaluates the worst 

case 90° shear condition (previous testing evaluated different angular offsets but this particular 

condition is the worst-case and most critical for modeling). 
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Figure 26. Three different notched tensile specimen geometries with a 2-inch gage length.
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Figure 27. Shear test specimen utilized for testing.

For reference, photographs of typical test setups are provided in Figure 28, highlighting the 

instrumentation utilized during testing. The instrumentation attached to the specimens in Figure 

28 are transducers designed to measure displacement on the specimen. Each test result was 

essentially a discrete listing of load and displacement that was subsequently analyzed to provide 

insight and results for the test.

0.025 0.475

0.06

0.4D

0.1D

0.250

0.175

0.387

0.025

0.125

1.25

1.0

1.25

5.50

2.0

1.0

4.00

Detail

A

Detail

B

Detail A – Clip Gage Recess Detail B – Center Section

0.5D

Shear Test Specimen Geometry – Plate Material

All specimens: 0.5-inch thick

*** NO SCALE***
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 (a)

 

(b)

(c)

Figure 28. Different test setups for (a) smooth, (b) notched, and (c) shear tests.

3.2 Overview of Results

The key data from this program for the modeling was the continuous load-displacement data 

recorded during the tests. Examples of the measured data for the smooth and notched round bar 

tensile tests are shown in Figure 29, Figure 30, and Figure 31 for the NUCU, HPS100W and 

A514B steels respectively. In these figures the load and displacement data have been converted 

to engineering stress-strain data for the tests. 
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Figure 29. Characterization test data for the ATCCRP NUCU Steel.

Figure 30. Characterization test data for the ATCCRP HPS100W Steel.
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Figure 31. Characterization test data for the ATCCRP A514B Steel.

In this section of the report, we provide primarily a tabular summary of the tests and the key data 

resulting from each test. Tabulated results for the Phase I testing are included in Table 12-Table 

14 and for Phase II in Table 15-Table 17. These critical continuous test data results will be 

provided in a subsequent section of this report when the data fits used in the analysis are 

presented.

3.2.1 Smooth Specimen Tensile Properties

A comparison of the average tensile properties measured for the non-TC128B material tested 

during Phase I is summarized in Figure 32 based upon the average data in Table 12. Several 

observations are apparent. First, the degree of observed anisotropy (difference between the two 

orientations) is very low. The materials are homogeneous, likely based on the fine grain 

microstructure apparent in these materials. The two highest strength steels, namely the A514B

and A709 Gr HPS100W, exhibit very similar properties with slightly higher strength and lower 

ductility observed in the A514B steel. Conversely the NUCU material (A710 Gr B) tensile 

properties in Figure 32 exhibit lower strength and higher ductility than the other two steels.
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Figure 32. Tensile property comparison of Phase I non-TC128B materials.

Tensile strain rate effects can be determined for the Phase I materials by comparing data in Table 

14. Strain rate makes no statistical impact on ductility; this is true if either the percent elongation 

or reduction of area data are compared in Table 14. The rate effects manifested by strength are 

fairly weak. For the non-TC128B materials in Table 14, the result of a higher rate is only 4-7 ksi 

in tensile strength (slightly higher impact on yield strength). Virtually no statistical increase in 

properties is noted for the Phase I TC128B tested at high rate.

The average tensile properties for the four different TC128B heats is shown in Figure 33 based 

on the data in Table 15. Note that the average values are for both orientations combined; the 

extent of anisotropy noted was negligible between the two orientations. On balance, little 

strength or ductility variation is apparent for any of these different TC128B heats. This suggests 

that sulfur content has a minimal impact on tensile properties. The lowest strength and highest 

ductility observed was for the Phase II T-material (low sulfur content and extracted from a tank 

car being built). Recall this material was subjected to a PWHT treatment since it had been 

curved into one of the tank car segments. It is unknown whether the slight difference in tensile 

properties for this material when compared to the other materials is a consequence of the PWHT 

or simply lot-to-lot variability.

L-orientation

Strength, ksi

0

20

40

60

80

100

120

Elongation, percent

0

10

20

30

40

50

60

UTS

YS

Elongation

T-orientation

A514B

NUCU

HPS100W

A514B

NUCU

HPS100W
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Figure 33. Tensile property comparison of Phase I and II TC128B materials.

Combined L- and T-orientation

Strength, ksi

0

15

30

45

60

75

90

105

120

Ductility, percent

0

10

20

30

40

50

60

70

80

UTS

YS

RA

Elongation

High S

(Phase 1)

Medium S

(Ph2: A-matl)

Low S

(Ph2: S-matl)

Low S

(Ph2: T-matl)
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Table 12. Measured tensile properties for both orientations (Phase I).

Material Orientation Specimen UTS, YS, Elong RA,

ID No. ksi ksi (2”GL),% %

TC128B

L

T-L-S-1 96 77 28 67

T-L-S-2 96 76 31 68

T

T-T-S-1 95 76 31 70

T-T-S-2 95 76 30 71

Average: 95.1 76.2 30.0 69.0

A514B

L

N-L-S-1 122 113 20 61

N-L-S-2 122 113 15 62

T

N-L-T-1 124 114 22 68

N-L-T-2 123 114 22 67

Average: 122.9 113.1 19.8 64.5

NUCU

L

A-L-S-1 94 62 26 57

A-L-S-2 95 62 26 57

T

A-T-S-1 98 65 25 50

A-T-S-2 95 64 27 55

Average: 95.5 62.9 26.0 54.8

HPS100W

L

H-L-S-1 121 109 >153 74

H-L-S-2 121 109 25 75

T

H-T-S-1 120 107 26 76

H-T-S-2 120 108 26 75

Average: 120.5 108.5 25.7 75.0

 3 Specimen failed outside gage length marks; value based on total length measurement
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Table 13. Notched tensile test results (L-orientation, Phase I).

Material

Specimen Notch Notch Max Net Max Bridging

ID No. D, inch R, inch Stress, ksi Strain (0.5” GL), in/in

TC128B

T-05-S-1 0.2508 0.0518 151.1 5.0

T-05-S-2 0.2502 0.0508 151.5 5.6

T-10-S-1 0.2506 0.1013 132.4 9.1

T-10-S-2 0.2498 0.1013 132.0 9.4

T-25-S-1 0.2512 0.2474 113.2 16.7

T-25-S-2 0.2507 0.2474 114.3 16.7

A514B

N-05-S-1 0.2510 0.0510 197.4 2.0

N-05-S-2 0.2506 0.0518 197.7 1.8

N-10-S-1 0.2510 0.1014 172.5 3.7

N-10-S-2 0.2507 0.1009 171.9 4.4

N-25-S-1 0.2507 0.2474 150.7 8.0

N-25-S-2 0.2511 0.2474 148.9 7.2

NUCU

A-05-S-1 0.2508 0.0507 145.5 4.3

A-05-S-2 0.2513 0.0508 145.4 3.6

A-10-S-1 0.2514 0.1011 128.2 7.0

A-10-S-2 0.2508 0.1010 127.3 7.1

A-25-S-1 0.2512 0.2476 111.3 12.7

A-25-S-2 0.2506 0.2472 113.3 8.9

HPS100W

H-05-S-1 0.2513 0.0510 194.1 4.3

H-05-S-2 0.2508 0.0512 194.5 4.4

H-10-S-1 0.2507 0.1012 168.2 8.9

H-10-S-2 0.2512 0.1010 168.6 7.5

H-25-S-1 0.2510 0.2472 145.6 17.1

H-25-S-2 0.2506 0.2474 146.9 16.2
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Table 14. Quasistatic and high rate tensile test results (L-orientation, Phase I).

Material Test Rate

Specimen UTS, YS, Elong RA,

ID No. ksi ksi (0.5”GL),% %

TC128B

quasistatic

T-Q-1 96.7 76.3 28 67

T-Q-2 95.5 75.4 26 65

intermediate

T-M-1 96.5 76.1 29 66

T-M-2 96.1 76.0 28 70

high-rate

T-O-1 96.9 79.8 26 66

T-O-2 101.6 84.0 27 66

A514B

quasistatic

N-Q-1 119.6 109.9 21 66

N-Q-2 120.0 110.4 21 64

intermediate

N-M-1 120.5 110.5 21 63

N-M-2 120.4 110.1 20 64

high-rate

N-O-1 126.9 118.3 21 63

N-O-2 126.7 118.5 20 60

NUCU

quasistatic

A-Q-1 94.8 60.2 22 53

A-Q-2 96.3 62.6 22 44

intermediate

A-M-1 95.0 61.3 26 47

A-M-2 95.6 61.8 28 56

high-rate

A-O-1 102.1 72.0 25 53

A-O-2 103.1 73.5 24 51

HPS100W

quasistatic

H-Q-1 119.3 106.5 24 74

H-Q-2 120.0 107.0 24 75

intermediate

H-M-1 120.0 107.3 25 74

H-M-2 119.3 106.2 25 75

high-rate

H-O-1 124.0 112.5 23 71

H-O-2 123.7 112.7 24 72
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Table 15. Measured tensile properties for the three TC128B variants in Phase II.

Material Orientation

Specimen UTS, YS, Elong RA,

ID No. ksi ksi (1”GL),% %

A-material

L

A-289-L1 93 67 33 68

A-289-L2 94 69 32 70

T

A-289-T1 94 67 34 66

A-289-T2 94 67 31 64

average: 93.8 67.7 32.7 66.8

S-material

L

S-288-L1 93 67 34 64

S-288-L2 92 68 31 63

T

S-288-T1 92 68 30 64

S-288-T2 92 68 29 63

average: 92.4 67.8 31.0 63.3

T-material

L

T-290-L1 86 62 31 70

T-290-L2 85 63 36 71

T

T-290-T1 85 61 35 71

T-290-T2 85 60 35 73

average: 85.1 61.3 34.3 71.2
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Table 16. Notched tensile results (L orientation) for the three TC128B variants in Phase II.

Material

Notch Specimen Max Net Axial Displ at Net Failure RA,

Radius, inch ID No. Stress, ksi Failure, inch Stress, ksi %

A-material

0.05

A-289-N05-L1 144 0.031 131 36

A-289-N05-L2 143 0.033 125 37

A-289-N05-L3 145 0.038 125 43

0.10

A-289-N10-L1 127 0.045 111 44

A-289-N10-L2 127 0.052 104 50

A-289-N10-L3 126 0052 104 49

0.25

A-289-N25-L1 111 0.080 86 56

A-289-N25-L2 111 0.095 82 63

A-289-N25-L3 109 0.087 84 57

S-material

0.05

S-288-N05-L1 143 0.037 122 48

S-288-N05-L2 141 0.036 122 49

0.10

S-288-N10-L1 125 0.052 102 47

S-288-N10-L2 123 0.047 100 48

0.25

S-288-N25-L1 109 0.083 86 53

S-288-N25-L2 108 0.090 81 57

T-material

0.05

T-290-N05-L1 131 0.047 106 52

T-290-N05-L2 130 0.045 107 53

0.10

T-290-N10-L1 117 0.059 90 54

T-290-N10-L2 115 0.064 88 54

0.25

T-290-N25-L1 102 0.103 71 76

T-290-N25-L2 101 0.103 71 70
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Table 17. Shear test results for the three TC128B variants in Phase II.

Material

Specimen Max Shear Axial Displ at Failure Shear

ID No. Stress, ksi Failure, inch Stress, ksi

A-material

A-289-S1 76 0.209 72

A-289-S2 77 0.190 75

S-material

S-288-S1 74 0.195 67

S-288-S2 74 0.200 68

T-material

T-290-S1 71 0.231 65

T-290-S2 71 0.229 63

3.2.2 Notched Specimen Tensile Properties

One way to examine notched strength test results is to quantify the notch strength ratio, defined 

as the ratio of the notch strength (maximum net stress incurred in the specimen) normalized by 

the ultimate strength of the material. These notch strength ratios are shown in Figure 34 (nonTC128B materials, based on the data in Table 13) and Figure 35 (TC128B materials, based on 

the data in Table 13 and Table 16).

The notched strength ratio in Figure 34 and Figure 35 indicates the conventional expected trend 

for all materials and heats. As notch acuity increases (the notch gets tighter and the stress 

concentration increases), the achieved notch strength also increases. For the tightest notches, the 

net stress is over 150% of the ultimate strength of the material. For the bluntest notches, the 

level falls to 120% of the ultimate strength of the material.

All seven test materials exhibited very similar trends and magnitudes of notch strength ratio as 

seen in Figures Figure 34 and Figure 35. In fact, the similarity in notched strength for the 

TC128B material (Figure 35) is remarkable, especially considering the medium and low sulfur 

heats. However, this similarity does not necessarily mean the load-strain response is similar, and 

this is something that will be addressed when the data are shown in the modeling section of this 

report.
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Figure 34. Notch strength comparison of Phase I non-TC128B materials.

Figure 35. Notch strength comparison of Phase I and II TC1288B materials.

A514B NUCU HPS100W

Notch Strength Ratio

0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

R = 0.05-inch notch

R = 0.10-inch notch

R = 0.25-inch notch

Notch Strength Ratio

0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

R = 0.05-inch notch

R = 0.10-inch notch

R = 0.25-inch notch

High S

(Phase 1)

Medium S

(Ph2: A-matl)

Low S

(Ph2: S-matl)

Low S

(Ph2: T-matl)
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Another way of examining notch data is shown in Figure 36 the notch ductility ratio, essentially 

the measured reduction of area in the notched specimen (see Table 16) divided by the reduction 

of area observed in the smooth specimen test. A close examination of the reduction of area data 

in Table 16 indicates that in the presence of the notch, the ductility typically stays the same or 

decreases; in the smooth tests, RA for TC128B varies between 65-75% whereas in the notched 

test it ranges from 35-70%. When the notch data is considered in this fashion, there are some 

differences observed in Figure 36. The most acute notch has the lowest ductility ratio value 

(essentially the acute notch is more severe and in the failure process consumes ductility) whereas 

in the case of the bluntest notch this ratio indicates a loss of 20% or less of the ductility. The 

most curious trend in Figure 36 is the markedly lower ductility ratio for the medium sulfur case 

when compared to the two low sulfur conditions.

Figure 36. Notch ductility ratio comparison of Phase II TC128B materials.

3.2.3 Shear Properties

Shear tests, performed only during the Phase II testing, were performed on three heats of 

TC128B as shown in Table 17 and Figure 37. The results are plotted in terms of shear-stress-toultimate-strength ratio in Figure 37. The shear ratio results fall into a relatively tight range of 

0.80-0.83 and do not appear to vary in any significant manner for the medium and low sulfur 

cases examined.

Notch Ductility (RA) Ratio

0.00

0.25

0.50

0.75

1.00

R = 0.05-inch notch

R = 0.10-inch notch

R = 0.25-inch notch Medium S (Ph2: A-matl)

Low S

(Ph2: S-matl)

Low S

(Ph2: T-matl)
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Figure 37. Shear strength comparison of Phase II TC128B materials.

3.3 Model Calibration for the Alternative Materials Characterized

A set of constitutive parameters were developed for each of the materials characterized in this 

program, as well as some TC128B materials characterized in previous tank car research 

programs. In this section, we present the material parameters and correlation of the model with 

test data for the non-TC128B materials tested in Phase I. The specific alloys and materials 

included in this study include the following:

• A709-Gr. HPS100W: moderate strength bridge steel (1-inch thick),

• NUCU: a higher strength bridge steel, nominally ASTM A710-GrB (0.5-inch thick), and,

• A514-GrB: current higher strength bridge steel (0.75-inch thick).

The baseline tensile test stress-strain behaviors for these materials are compared to each other 

and the Phase I TC128B in Figure 38. The plot shows that the NUCU material is similar in 

character to a TC128B material. Note that the Phase I TC128B Material has a significantly 

higher yield stress and a higher ultimate stress than any other TC128B material characterized to 

date in the NGRTC or ATCCRP Programs. The other two materials are higher in strength and 

very similar to each other with yield stresses of approximately 110 ksi and ultimate stresses of 

approximately 120 ksi. The comparison of the measured and calculated material behaviors are 

presented in the following subsections. Shear/UTS Ratio (

σshear/UTS)

0.00

0.25

0.50

0.75

1.00

Medium S

(Ph2: A-matl)

Low S

(Ph2: S-matl)

Low S

(Ph2: T-matl)
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Figure 38. Comparison of tensile test stress-strain behaviors for the Phase I materials.

3.3.1 NUCU Material Properties 

The material constitutive and damage model parameters can be developed primarily from the

series of smooth and notched round bar tensile tests. The initial true stress versus true strain 

curve is developed from the smoothed round bar tensile test. Subsequent analyses of the notched 

tensile test allow for the determination of the Drucker Prager pressure effects coefficient and the 

corresponding Bao-Wierzbicki damage parameters. The final set of constitutive parameters are 

then used to simulate the set of smooth and notched tensile tests to validate that the constitutive 

model parameters have been properly determined and to show the quality of the correlation 

between the model and test data. 

The constitutive parameters for NUCU are summarized in Table 18 and the correlation of the 

material constitutive model and material calibration tensile test data is shown in Figure 39. For 

this material, the traditional Bao-Wierzbicki Model (n=1.00) provided a good fit to the measured 

ductility over the range of stress triaxialities in the tests. The effect of mean stress on the yield 

behavior is also relatively low for this material (compared to the other materials in this study) 

with a Drucker-Prager yield criterion coefficient (α) equal to 0.015. 
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Table 18. Material constitutive parameters and tabular NUCU stress-strain values

Material Constitutive Parameters

Bao Wierzbicki Coefficient - A 0.75

Bao Wierzbicki Coefficient - B 1.10

Modified Bao Wierzbicki Coefficient - n 1.00

Drucker Prager Coefficient - α 0.015

Point No. Plastic Strain (in/in) True Stress (ksi)

1 0.000e+00 66.5

2 1.810e-03 61.7

3 1.010e-02 63.5

4 1.980e-02 74.6

5 3.740e-02 86.0

6 6.060e-02 96.0

7 9.900e-02 104.2

8 1.438e-01 109.3

9 2.457e-01 116.6

10 3.950e-01 123.6

11 1.390e-00 155.8
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Figure 39. Model calibration for the ATCCRP NUCU Steel.

3.3.2 HPS100W Material Properties 

The constitutive parameters for HPS100W are summarized in Table 19 and the correlation of the 

material constitutive model and material calibration tensile test data is shown in Figure 40. For 

this material, the Modified Bao-Wierzbicki Model was required to predict the ductility for the 

higher triaxiality levels (n=1.60). The effect of mean stress on the yield behavior is moderate for 

this material (compared to the other materials in this study) with a Drucker-Prager yield criterion 

coefficient (α) equal to 0.045. 
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Table 19. Material constitutive parameters and tabular HPS100W stress-strain values

Material Constitutive Parameters

Bao Wierzbicki Coefficient - A 1.40

Bao Wierzbicki Coefficient - B 3.60

Modified Bao Wierzbicki Coefficient - n 1.60

Drucker Prager Coefficient - α 0.045

Point No. Plastic Strain (in/in) True Stress (ksi)

1 0.00E+00 109.6

2 6.50E-04 111.1

3 2.48E-03 112.2

4 6.06E-03 114.1

5 1.95E-02 119.2

6 3.55E-02 124.8

7 5.83E-02 130.6

8 8.52E-02 135.0

9 1.45E-01 140.0

10 2.94E-01 151.2

11 1.29E+00 203.0
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Figure 40. Model calibration for the ATCCRP HPS100W Steel.

3.3.3 A514B Material Properties 

The constitutive parameters for A514B are summarized in Table 20 and the correlation of the 

material constitutive model and material calibration tensile test data is shown in Figure 41. For 

this material, the Modified Bao-Wierzbicki Model was required to predict the ductility for the 

higher triaxiality levels (n=2.20). The effect of mean stress on the yield behavior is moderate for 

this material (compared to the other materials in this study) with a Drucker-Prager yield criterion 

coefficient (α) equal to 0.035. 
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Table 20. Material constitutive parameters and tabular A514B stress-strain values

Material Constitutive Parameters

Bao Wierzbicki Coefficient - A 1.20

Bao Wierzbicki Coefficient - B 3.00

Modified Bao Wierzbicki Coefficient - n 2.20

Drucker Prager Coefficient - α 0.035

Point No. Plastic Strain (in/in) True Stress (ksi)

1 0.00E+00 117.5

2 4.20E-04 114.5

3 1.29E-02 116.6

4 2.31E-02 121.2

5 3.71E-02 126.5

6 5.57E-02 131.4

7 8.51E-02 135.0

8 1.25E-01 137.6

9 1.95E-01 141.1

10 2.94E-01 145.2

11 1.29E+00 182.1
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Figure 41. Model Calibration for the ATCCRP A514B Steel.

3.4 Evaluation of TC128B Steel samples

In addition to characterizing alternative steels, tests and analyses were performed on various 

samples of TC128B to investigate variability and where possible correlations to composition. It 

has been previously observed that there can be significant variations in the mechanical properties 

of TC128B. For example, the tensile stress-strain properties of the TC128B Samples tested in 

this program are compared to several other samples from previous research programs in Figure 

42. These various samples have yield strengths ranging from approximately 55 ksi to over 75 ksi 

and ultimate strengths of 83 to 95 ksi. 

In addition to the TC128B samples characterized in this research program, previous sets of 

TC128B characterization test data were available from the NGRTC research program [1-8]. 

These material data sets were reexamined and updated constitutive parameters were developed 

that include the Drucker Prager yield effects and modified Bao Wierzbicki damage model. The 

re-characterization and model comparisons for these materials are included in the following 

section of the report. 
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Figure 42. Comparison of tensile stress-strain curves from various TC128B samples.

3.4.1 NGRTC TC128B Material Properties 

The material samples characterized in the NGRTC program included:

• two older TC128B plate samples that were removed from the tank cars used for the fullscale side impact tests (Tank Cars 3069 and 3074 materials) 

• new (vintage 2007) sample of normalized TC128B (0.777-inch-thick). 

The two older plate samples were at the lower end of the strength scale for the range of TC128B 

materials tested and the new TC128B sample had a significantly higher strength. The 

comparison of the tensile data for the new material with one of the older tank car samples is 

provided in Figure 43. 

3.4.1.1 NGRTC Tank Car 3069 TC128B Material Properties 

The first of the NGRTC TC128B samples characterized was an older material recovered from 

the test tank car Number 3069. A full set of smooth and notched tensile tests was performed for 

this material and the tensile test data is summarized in Figure 44. 
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Figure 43. Comparison of tank car puncture analyses with different failure criteria.

Figure 44. Characterization test data for the NGRTC Tank Car 3069 TC128B plate.
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The constitutive parameters for the Tank Car 3069 TC128B material are summarized in Table 21

and the correlation of the constitutive model and tensile test data is shown in Figure 45. For this 

material, the traditional Bao-Wierzbicki Model (n=1.00) was used. However the comparison of 

the calculated and measured ductility over the range of stress triaxialities in the tests suggests 

that a better fit could be obtained with a higher value of a modified Bao-Wierzbicki exponent 

(n). The effect of mean stress on the yield behavior is also relatively high for this material 

(compared to the other materials in this study) with a Drucker-Prager yield criterion coefficient 

(α) equal to 0.120. 

Table 21. Material constitutive parameters and tabular stress-strain values for the 

Tank Car 3069 TC128B

Material Constitutive Parameters

Bao Wierzbicki Coefficient - A 0.75

Bao Wierzbicki Coefficient - B 2.00

Modified Bao Wierzbicki Coefficient - n 1.00

Drucker Prager Coefficient - α 0.120

Point No. Plastic Strain (in/in) True Stress (ksi)

1 0.00E+00 54.7

2 4.00E-03 54.9

3 2.74E-02 72.5

4 5.40E-02 84.6

5 8.67E-02 92.7

6 1.46E-01 100.0

7 2.60E-01 110.0

8 5.00E-01 128.0

9 1.00E+00 157.0

10 2.44E+00 220.0
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Figure 45. Model calibration for the NGRTC Tank Car 3069 TC128B plate.

3.4.1.2 NGRTC Tank Car 3074 TC128B Material Properties 

The second of the NGRTC TC128B samples characterized was an older material recovered from 

the test tank car Number 3074. A full set of smooth and notched tensile tests was performed for 

this material and the tensile test data is summarized in Figure 46. 

The constitutive parameters for the Tank Car 3074 TC128B material are summarized in Table 22

and the correlation of the constitutive model and tensile test data is shown in Figure 47. For this 

material, the traditional Bao-Wierzbicki Model (n=1.00) provided a good fit to the measured 

ductility over the range of stress triaxialities in the tests. The effect of mean stress on the yield 

behavior is moderate for this material (compared to the other materials in this study) with a 

Drucker-Prager yield criterion coefficient (α) equal to 0.050. 
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Figure 46. Characterization test data for the NGRTC Tank Car 3074 TC128B plate.

Figure 47. Model calibration for the NGRTC Tank Car 3074 TC128B plate.
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Table 22. Material constitutive parameters and tabular stress-strain values for the 

Tank Car 3074 TC128B

Material Constitutive Parameters

Bao Wierzbicki Coefficient - A 0.75

Bao Wierzbicki Coefficient - B 2.00

Modified Bao Wierzbicki Coefficient - n 1.00

Drucker Prager Coefficient - α 0.050

Point No. Plastic Strain (in/in) True Stress (ksi)

1 0.00E+00 58.5

2 1.20E-03 55.1

3 1.30E-02 55.3

4 2.76E-02 67.1

5 5.41E-02 80.2

6 9.87E-02 90.9

7 1.58E-01 97.9

8 2.50E-01 105.5

9 8.55E-01 140.0

10 2.17E+00 170.0

3.4.1.3 NGRTC Tank Car New Normalized 0.777-inch TC128B Plate Material Properties 

The third of the NGRTC TC128B samples characterized was a section from a 0.777-inch-thick 

plate of new TC128B material that was normalized. A full set of smooth and notched tensile 

tests was performed for this material and the tensile test data is summarized in Figure 48. 
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Figure 48. Characterization test data for the NGRTC new normalized 0.777-inch TC128B plate.

The constitutive parameters for the 0.777-inch-thick plate of new TC128B are summarized in 

Table 23 and the correlation of the material constitutive model and material calibration tensile 

test data is shown in Figure 49. For this material, the traditional Bao-Wierzbicki Model (n=1.00) 

provided a good fit to the measured ductility over the range of stress triaxialities in the tests. The 

effect of mean stress on the yield behavior is quite high for this material (compared to the other 

materials in this study) with a Drucker-Prager yield criterion coefficient (α) equal to 0.195. 

Tank Car 3069 TC128B Material Characterization & Model Calibration -Figure 49. Modified 

Bao-Wierzbicki Model (n=1.00), Drucker-Prager Yield Criterion (a=0.195), High Resolution 

Analysis
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Table 23. Material constitutive parameters and tabular stress-strain values for the new 

normalized 0.777-inch TC128B

Material Constitutive Parameters

Bao Wierzbicki Coefficient - A 0.75

Bao Wierzbicki Coefficient - B 2.00

Modified Bao Wierzbicki Coefficient - n 1.00

Drucker Prager Coefficient - α 0.195

Point No. Plastic Strain (in/in) True Stress (ksi)

1 0.00E+00 73.4

2 1.52E-03 70.0

3 1.05E-02 69.1

4 2.22E-02 82.2

5 5.36E-02 100.2

6 9.82E-02 111.8

7 1.50E-01 118.5

8 2.50E-01 128.5

9 5.00E-01 143.5

10 1.25E+00 180.0
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Figure 49. Model calibration for the NGRTC new normalized 0.777-inch TC128B plate.

3.4.2 ATCCRP TC128B Material Properties 

The first of the ATCCRP TC128B materials was a sample of 0.750-inch-thick plate and was 

tested as part of the Phase I test program (shown previously in Figure 38). A full set of smooth 

and notched tensile tests was performed for this material and the tensile test data is summarized 

in Figure 50. 

The constitutive parameters for the 0.750-inch-thick TC128B plate are summarized in Table 24

and the correlation of the material constitutive model and material calibration tensile test data is 

shown in Figure 51. For this material, the traditional Bao-Wierzbicki Model (n=1.00) provided a 

good fit to the measured ductility over the range of stress triaxialities in the tests. The effect of 

mean stress on the yield behavior is moderate for this material (compared to the other materials 

in this study) with a Drucker-Prager yield criterion coefficient (α) equal to 0.040. 

The other three ATCCRP TC128B materials were tested in Phase II and were chosen with an 

emphasis on evaluating the effects of reduced sulfur levels on the material performance. The 

first of these three was the Arcelor Medium Sulfur TC128B plate. A full set of smooth and 

notched tensile tests was performed for this material and the tensile test data is summarized in 

Figure 52. 
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Figure 50. Characterization test data for the baseline ATCCRP 0.750-inch TC128B plate.

Figure 51. Model calibration for the baseline ATCCRP 0.750-inch TC128B plate.
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Table 24. Material constitutive parameters and tabular stress-strain values for the 

ATCCRP 0.750-inch TC128B

Material Constitutive Parameters

Bao Wierzbicki Coefficient - A 1.20

Bao Wierzbicki Coefficient - B 1.80

Modified Bao Wierzbicki Coefficient - n 1.00

Drucker Prager Coefficient - α 0.040

Point No. Plastic Strain (in/in) True Stress (ksi)

1 0.00E+00 79.6

2 1.51E-03 78.3

3 5.91E-03 79.0

4 2.38E-02 88.3

5 4.10E-02 94.8

6 6.32E-02 101.5

7 1.03E-01 107.9

8 1.44E-01 112.3

9 2.96E-01 126.7

10 4.45E-01 136.8

11 1.49E+00 177.3

The constitutive parameters for the Arcelor Medium Sulfur TC128B plate are summarized in 

Table 25 and the correlation of the material constitutive model and material calibration tensile 

test data is shown in Figure 53. For this material, the Modified Bao-Wierzbicki Model was 

required to predict the ductility for the higher triaxiality levels (n=1.50). The effect of mean 

stress on the yield behavior is moderate for this material (compared to the other materials in this 

study) with a Drucker-Prager yield criterion coefficient (α) equal to 0.050. 
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Figure 52. Characterization test data for the baseline ATCCRP Arcelor Medium Sulfur TC128B 

plate.

Figure 53. Model calibration for the Arcelor Medium Sulfur TC128B plate.
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Table 25. Material constitutive parameters and tabular stress-strain values for the 

Arcelor Medium Sulfur TC128B

Material Constitutive Parameters

Bao Wierzbicki Coefficient - A 1.00

Bao Wierzbicki Coefficient - B 1.50

Modified Bao Wierzbicki Coefficient - n 1.00

Drucker Prager Coefficient - α 0.050

Point No. Plastic Strain (in/in) True Stress (ksi)

1 0.00E+00 72.0

2 5.89E-04 67.7

3 3.52E-03 69.5

4 1.45E-02 69.5

5 3.20E-02 84.4

6 6.16E-02 96.3

7 1.06E-01 105.7

8 1.71E-01 112.9

9 3.46E-01 126.0

10 7.00E-01 142.5

11 2.09E+00 175.0

The second ATCCRP TC128B material tested in Phase II was the SSAB Low Sulfur TC128B 

plate. A full set of smooth and notched tensile tests was performed for this material and the 

tensile test data is summarized in Figure 54. 

The constitutive parameters for the SSAB Low Sulfur TC128B plate are summarized in Table 26

and the correlation of the material constitutive model and material calibration tensile test data is 

shown in Figure 55. For this material, the Modified Bao-Wierzbicki Model was required to 

predict the ductility for the higher triaxiality levels (n=1.60). The effect of mean stress on the 

yield behavior is moderate for this material (compared to the other materials in this study) with a 

Drucker-Prager yield criterion coefficient (α) equal to 0.050. 
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Figure 54. Characterization test data for the baseline ATCCRP SSAB Low Sulfur TC128B plate.

Figure 55. Model calibration for the SSAB Low Sulfur TC128B plate.
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Table 26. Material constitutive parameters and tabular stress-strain values for the 

SSAB Low Sulfur TC128B

Material Constitutive Parameters

Bao Wierzbicki Coefficient - A 1.40

Bao Wierzbicki Coefficient - B 3.75

Modified Bao Wierzbicki Coefficient - n 1.60

Drucker Prager Coefficient - α 0.050

Point No. Plastic Strain (in/in) True Stress (ksi)

1 0.00E+00 71.5

2 3.88E-04 69.3

3 1.15E-02 69.2

4 1.73E-02 75.0

5 3.69E-02 87.0

6 6.65E-02 96.7

7 9.63E-02 102.2

8 1.24E-01 106.0

9 1.56E-01 109.1

10 2.96E-01 122.0

11 1.99E+00 194.0

The third ATCCRP TC128B material tested in Phase II was the Trinity Low Sulfur TC128B 

plate. A full set of smooth and notched tensile tests was performed for this material and the 

tensile test data is summarized in Figure 56. 

The constitutive parameters for the Trinity Low Sulfur TC128B plate are summarized in Table 

27 and the correlation of the material constitutive model and material calibration tensile test data 

is shown in Figure 57. For this material, the traditional Bao-Wierzbicki Model (n=1.00) 

provided a good fit to the measured ductility over the range of stress triaxialities in the tests. The 

effect of mean stress on the yield behavior is moderate for this material (compared to the other 

materials in this study) with a Drucker-Prager yield criterion coefficient (α) equal to 0.050. 
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Figure 56. Characterization test data for the baseline ATCCRP Trinity Low Sulfur TC128B plate.

Figure 57. Model calibration for the Trinity Low Sulfur TC128B plate.
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Table 27. Material constitutive parameters and tabular stress-strain values for the 

Trinity Low Sulfur TC128B

Material Constitutive Parameters

Bao Wierzbicki Coefficient - A 0.85

Bao Wierzbicki Coefficient - B 2.20

Modified Bao Wierzbicki Coefficient - n 1.00

Drucker Prager Coefficient - α 0.050

Point No. Plastic Strain (in/in) True Stress (ksi)

1 0.00E+00 64.5

2 1.17E-03 62.1

3 1.77E-02 64.0

4 2.06E-02 66.9

5 2.74E-02 72.0

6 4.11E-02 79.0

7 6.05E-02 86.1

8 9.14E-02 92.9

9 1.31E-01 98.0

10 3.56E-01 119.2

11 5.63E-01 131.0

12 1.18E+00 153.0

3.5 Evaluation of Puncture Resistance for Alternative Tank Car Materials

An objective of this project is to assess the combination of material properties that will guide the 

search for optimization of the tank car material selection. To assist in this effort we evaluated

the puncture performance of a set of candidate steels with significantly different properties from 

TC128B as shown in Figure 58. Note that these candidate steels were selected based on their 

mechanical properties and availability of test data and not necessarily for their suitability for use 

in railroad tank car service (e.g. weldability, fatigue resistance, cost). The idea is that once the 
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desirable mechanical properties were identified, the selection of a tank car material that 

optimizes the desirable properties could be identified. 

Figure 58. Candidate tank car steels with a range of mechanical properties.

The methodology that will be applied is:

1. Use existing data to develop constitutive and BW failure parameters and validate against 

material test data. 

2. Simulate a series of side impact puncture conditions on a 105J600I chlorine tank car design 

with each candidate material. Compare results to the corresponding TC128B tank car 

design. 

3. Evaluate the comparisons of the different materials to assess the influence of various 

material characteristics (e.g. yield, ultimate, elongation) on puncture resistance. 
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3.5.1 Tank Car Puncture Modeling

The BW failure models and constitutive model fits developed in this program can be used with 

the previously developed tank car puncture prediction capability to assess the material effects on 

puncture performance. This tank car impact and puncture modeling capability was previously

developed and applied in multiple studies [1, 50] to evaluate a wide range of tank designs. The 

side impact condition was a normal impact centered on the belt line of the tank. 

The baseline failure models use a fine mesh of solid brick elements in the impact zone with an 

element dimension of approximately 0.040 inch (1 mm). The mesh transitions to shell elements 

outside the impact zone with increasing mesh coarseness. The model of the commodity tank and 

BW impact zone mesh used in the tank shell puncture analyses is shown in Figure 59. An 

existing algorithm in LS-DYNA is used to tie the edge of the shell elements to the solid elements 

around the edge of the impact zone. 

Figure 59. Tank model and impact zone mesh used for side impact puncture analyses.

As a result of the very fine mesh in the impact zone, the puncture models were significantly 

larger and have correspondingly longer run times. To allow for the evaluation of a wide range of 

impact conditions and tank geometries, some simplifications in the tank model were 

implemented. 
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The first simplification was the use of symmetry planes. For the majority of side impact 

analyses described in this section, two symmetry planes were used to reduce the model to onequarter of the full tank (a half model was used for the offset head impacts). This had a small 

effect since some tank car structural details could not be included in the quarter model (e.g. 

manway and bolsters). The primary effect of this approximation was that a side impact centered 

on the tank may have a slightly reduced stiffness for large dent sizes since the manway and 

surrounding structures are stiffer than the bare commodity tank. 

An example impact and puncture simulation is shown in Figure 60. The tank is backed by a 

rigid wall and impacted with a rigid impactor. Due to the vertical symmetry appproximation, no 

gravitational loads are applied. The tank is deformed locally by the impact and when sufficiently 

large impact forces develop, the impactor punctures the tank. A detailed view of the puncture 

behavior is shown in Figure 61. 

 

(a) Initial impact geometry (b) Puncture response of the tank

Figure 60. Detailed impact and puncture sequence for a 600 lb chlorine car.

(a) Initial impact deformations (b) Tank puncture response 

Figure 61. Calculated puncture initiation and fracture progression.
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The first set of analyses used 3x3, 3x6, 6x6, 9x9, 12x12, 3x12, 12x3 rectangular impactors, all 

with a 0.50-inch radius around the edges. The third set of tank impact analyses performed used 

round impactor face profiles to investigate the effects of the impactor shape. The additional 

impactors used were a 5.73, 7.64, 9.55, 11.46, and 13.37 inch diameter impactors (ram face 

perimeter lengths of 18, 24, 30, 36, and 42 inch, respectively). 

The calculated puncture forces and puncture energies for the various materials and various 

impactors in normal side impact conditions are summarized in Figure 62 and Figure 63, 

respectively. The puncture parameters in the figures are plotted against the impactor 

“characteristic size” defined as the square root of the area of the impactor face [50]. This 

parameter was found to be a good surrogate of impactor puncture threat for different impactor 

shapes. The fits to the data provide some insight to the relative performance for these impacts. 

However, we need a methodology that can summarize the relative performance of all of the 

impact conditions analyzed in a simpler format. 

The methodology selected to compare the relative performance of each material was to 

normalize the puncture performance metrics (force and energy) for each impact condition to the 

corresponding performance of the TC128B tank under the identical impact conditions as 

described in Equations 29 and 30. In the equation, the subscript (i) corresponds to the index 

number of the specific impact scenario being analyzed. 

FFnn1 = FFii

FFii

TTTT128BB (29)

EEnn1 = EEii

EEii

TTTT128BB (30)

These summaries of the normalized puncture forces and energies for all of the impact analyses 

performed are summarized in Figure 64 and Figure 65, respectively. It is interesting to note that 

the relative improvements in puncture force and puncture energy are not proportional for 

different candidate materials. For example, the 304L stainless produces the highest average 

normalized puncture energy (55% improvement over TC128B) but only a 17% improvement in 

average normalized puncture force which is less than three other materials (HY-100, A709 

HPS100, and HY-130). The relative improvements in the puncture forces and puncture energies 

from the different materials are also reasonably consistent across the range of different impactor 

sizes and shapes analyzed. 
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Figure 62. Calculated puncture forces for candidate tank car steels.

Figure 63. Calculated puncture energies for candidate tank car steels.
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Figure 64. Relative puncture force performance for candidate tank car steels.

Figure 65. Relative puncture energy performance for candidate tank car steels.
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The normalized puncture energies are overlayed with the corresponding normalized curve of 

impact energy versus normalized speed in Figure 66. The values correspond to an approximately 

6% reduction in puncture speed for A516-70 material and a 24% increase in puncture speed for 

the 304L stainless steel. Note that these values are for the idealized impact scenario restrained 

by the rigid impact wall. The corresponding variations in puncture probabilities for real world 

impact conditions may be considerably different. 

Figure 66. Relative puncture protection performance for candidate tank car steels.

3.6 Tank Car Puncture Modeling

The work presented so far has included results from extensive computer simulations of puncture 

performance as well as experimental results detailing the properties of a variety of different 

materials. The purpose of this section is to re-examine the computer simulations of puncture in 

the context of the impact of the different stress-strain properties derived for the materials.

3.6.1 Description of Different Stress-Strain Curve Parameters

Prior to examining the modeling results in the context of different material properties, it is useful 

to review the basic data obtained from a material strength test. A representative stress-strain 

curve for a material is shown in Figure 67 denoting several key quantities that are used to 

characterize the tensile response, specifically the strength and ductility, of the material. The 

typical key parameters from a tensile test include the yield strength (usually 0.2% strain offset), 
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the ultimate strength and the elongation at failure or rupture (denoted σYY, σUU and eeRR in Figure 

67). Although other parameters are sometimes included (for instance stiffness, or modulus, and 

another measure of ductility, reduction of area), these are the key parameters typically used to 

quantify tensile behavior.

Figure 67. Definition of the characterization of a material’s stress-strain behavior.

The yield and ultimate strength (as well as modulus) are considered material properties, 

somewhat independent of test method, given that typical test methodologies have been used to 

derive these properties. However, the ductility measurement, percent elongation, is a structural 

quantity (not a material property) that depends on the method used to measure it. For instance, 

the gage length of the specimen as well as the shape of the specimen used to measure percent 

elongation can affect elongation results (as recognized by Barba’s law, J. Barba, 1880). This 

non-property (e.g. non-unique) aspect of elongation is an issue that needs to be kept in mind 

when potentially using elongation as a correlating variable.

One other parameter shown in Figure 67 is the flow stress, defined for convenience as the 

average between yield and ultimate strength, which can be useful for providing a measure of the 

area under a stress strain curve. When predicting the energy to puncture, it is not unreasonable 

to relate this to an energy measure derived from the elastic and plastic strain-energy in a tensile 

test. However, rather than including all of the energy to rupture in a tensile test (in mechanics, 

this energy, or work, to rupture is termed the modulus of toughness), only the energy under the 

stress-strain curve to the ultimate stress will be utilized. This area, shaded in Figure 67, 

corresponds to the product of flow stress and elongation at ultimate, symbolically eeUUσff ffff.

Structural modeling experience has indicated that little energy is added after peak load is 

achieved.
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3.6.2 Influence of Stress-Strain Parameters on Puncture Force

In Section 3.5 of this report we have determined the relative puncture protection levels for a 

range of material types with diverse mechanical properties. However, it is desirable to evaluate 

the results and develop a predictive model using stress-strain characteristics (e.g. yield strength, 

ultimate strength, elongation). This model could then be applied to assess the performance of 

candidate materials and guide the selection or development of new materials. However, before 

developing the final form of the model, it is beneficial to examine how some of these different 

stress-strain parameters affect puncture force.

A quick review of the puncture performance and material properties indicates that the material 

ultimate strength is a significant factor for improving puncture resistance. However the 

performance is not proportional to only the material ultimate strength. A clear example of this 

can be seen by the comparison of the performance for TC128B and HY-80 tanks. The 

comparison of the TC128B and HY-80 material tensile stress-strain curves is shown in Figure 

68. The ultimate strength of the HY-80 is approximately 13 ksi higher than the ultimate strength 

of TC128B (96 ksi versus 83 ksi). Similarly, the yield strength of the HY-80 is approximately 

29 ksi higher than the yield strength of TC128B (84 ksi versus 55 ksi). However, in spite of the 

higher strength of HY-80 compared to TC128B, the average puncture energy for the HY-80 

tanks was lower than that of the TC128B tanks in the evaluation of puncture performance 

described previously (on average, puncture energy for HY-80 was 0.89 as shown in Figure 65, 

11% lower than that observed for TC128B). 

After evaluating the tank impact and puncture behaviors using a variety of models and 

methodologies, we have found that the impact and puncture performance can be primarily 

determined based on yield strength and ultimate strength. However, yield and ultimate strength 

only partially quantify the tensile behavior of the material; therefore, it may also be important to 

include a term in the model that quantifies the ductility of the material. In this modeling, the 

effect of ductility will be examined by including elongation at ultimate strength as well as a form 

that examines the strain energy in a stress-strain curve up to the ultimate strength of the material. 

However, before the form of the model is developed, the effect of these different parameters on 

puncture force will be determined in this section. 

The evaluation of the puncture performance, described in Section 3.5 is based on a series of side 

impact analyses with various impactors at both normal and oblique impact orientations. Each 

unique impact calculation with a specific tank material and impact condition results in a 

calculated force deflection behavior for the impactor up to the point at which the tank punctures 

(at the peak puncture force level). We integrate the impactor force-deflection curve up to the 

point of tank puncture to calculate the impact energy dissipated (puncture energy). 
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Figure 68. Comparison of the TC128B and HY-80 material tensile stress-strain curves.

The first significant assumption (observation) of the strength model for material performance is 

that the puncture force for a given impact scenario scales primarily with the ultimate strength. A 

summary of the relative puncture forces for all of the side impact calculations was provided 

previously in Figure 64. Remember that this data is the Fn1 force to puncture the tank scaled 

relative to the force required to puncture a TC128B tank under identical impact conditions. The 

average of normalized puncture force over the 18 impact conditions analyzed varies from 0.86 

for A516-70 to 1.48 for HT-130. We can demonstrate the influence of ultimate strength on the 

puncture force by creating a second normalized force that is equivalent to the previous 

normalized puncture force and scaled by the ratio of the TC128B ultimate strength to the specific 

material ultimate strength. This normalized force is defined below in Equation 31,

FFnn2 = FFii

FFii

TTTT128BB �

σσuu

TTTT128BB

σσuu

MMMMMM MM MMMM� (31)

with tabulated results shown in Table 28 and the UTS-corrected Fn2 plotted in Figure 69.
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Table 28. Baseline normalized puncture force scaled with different stress-strain parameters.

Material

Average Normalized (to TC128B) Puncture Force

Baseline σUU-corrected σYY-corrected eeUU-corrected eeUUσff ffff-corrected

Fn1 Fn2 Fn3 Fn4 Fn5

HY-130 1.48 0.88 0.63 3.38 1.74

HY-100 1.18 0.87 0.67 2.10 1.39

HY-80 1.06 0.93 0.73 1.14 1.12

SS 304L 1.17 1.01 1.66 0.43 0.44

A516-70 0.86 1.00 1.04 0.76 0.91

A709 HPS100 1.36 0.94 0.73 2.42 1.51

average: 1.19 0.94 0.91 1.71 1.19

std. dev.: 0.22 0.06 0.40 1.12 0.47

min: 0.86 0.87 0.63 0.43 0.44

max: 1.48 1.01 1.66 3.38 1.74

Figure 69. Relative puncture force after ultimate stress correction
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The scaling of the puncture forces by the material ultimate strength, shown in Figure 69, 

significantly reduces the variability in the calculated results (compare to Figure 64). The 

statistical assessment in Table 28 indicates that standard deviation of the normalized puncture 

force results is reduced by almost a factor of 4 (compare Fn1 to Fn2, standard deviation reduced 

from 0.22 to 0.06). This is an indication that the majority of the variation in puncture force is 

attributable to the material ultimate strength. This is also consistent with a punch-shear failure 

mechanism where the failure is dominated by exceeding the material strength around the 

perimeter of the impactor face.

As a further demonstration that the ultimate strength is the most significant factor on the 

puncture force, yet another normalized force was created that is equivalent to the first normalized 

puncture force and scaled by the ratio of the TC128B yield strength to the specific material yield 

strength. This normalized force is defined in Equation 32,

FFnn3 = FFii

FFii

TTTT128BB �

σσyy

TTTT128BB

σσyy

MMMMMM MM MMMM� (32)

with tabulated results shown in Table 28 and the YS-corrected Fn3 plotted in Figure 70. Whereas 

the ultimate strength correction in Figure 69 resulted in lower variability, the data in Table 28

indicates that variability of the data increases when a yield strength correction is applied. 

Specifically, the standard deviation nearly doubles (compare Fn1 to Fn3, standard deviation 

increases from 0.22 to 0.40). Given this, the scaling of the puncture forces by the material yield 

strength does not reduce the variability in the calculated results. This suggests that normalized 

puncture force varies primarily with tensile strength and less with yield strength (note that this 

approach looks at the trend with each variable alone, and not a combination of the two effects).

Although yield strength correlates less well than tensile strength, it does have a significant 

impact on the force deflection curve. This leads to the second significant assumption 

(observation) of the strength model for material performance is that the impact force deflection 

curve for a given impact scenario scales primarily with the yield strength. The impact force 

deflection behavior will have components that are controlled by the tank elastic modulus or 

internal pressure effects as well as a portion that is dominated by the plastic yielding around the 

dent. It is assumed that the plastic portion of the impact behavior is controlled by the yield stress 

at low plastic strain levels. 

To demonstrate this effect, consider the set of force-deflection curves for a normal impact with 

the six inch square impactor on the tanks of the various candidate materials as shown in Figure 

71. The curves all show similar behaviors but the magnitude of the force deflection curve is 

scaled up or down with a ranking order that is similar to the yield strength ranking. 
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Figure 70. Relative puncture force after yield stress correction

Figure 71. Calculated force deflection curve for various material tanks.

One of the issues in evaluating the yield strength effects is to determine the portion of the 

behavior that is controlled by the elastic response and the proportion of the curve dominated by 

the plastic behavior. With a relatively simple trial and error procedure we determined that 
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approximately 55% of the behavior is controlled by the elastic behavior and 45% is controlled by 

the plastic response. Thus we can define a yield stress corrected force by the equation:

FFyy = 0.55FF + 0.45FF �

σσyy

TTTT128BB

σσyy

MMMMMM MM MMMM� (33)

Using this equation, a plot of the yield strength corrected force-deflection curves for a normal 

impact with the six inch square impactor on the tanks of the various candidate materials is shown 

in Figure 72. When comparing Figure 71 and Figure 72, the yield corrected impact force (Figure 

72) tends to collapse the dispersed data onto a single characteristic, corrected force deflection 

curve. The points at which the tank is punctured vary as expected based on the material ultimate 

strengths. The one curve that diverges at the higher displacements in Figure 72 is the 304L 

stainless steel tank. It is believed that this is a consequence of the significant strain hardening of 

this material at relatively low strain levels increasing the level of force in the large deflection 

portion of the curve. Although the yield corrected impact force does a reasonable job collapsing 

the data, the outlier for stainless steel suggests that not all of the different material behaviors are 

captured by yield strength effects alone. Given that, this indicates a potential need for including 

an additional stress-strain characterization parameter, perhaps ductility (elongation).

Figure 72. Calculated force deflection curve for various materials with yield stress corrections.
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The preceding evaluations have used a method to illustrate how puncture force differences for 

the different materials scale with strength (ultimate and yield). A similar technique can be used 

to examine how puncture force varies with the two additional (ductility-based) tensile parameters 

discussed earlier: percent elongation at ultimate and area under the stress-strain curve up until 

ultimate strength. Again, using a similar approach as to that discussed earlier, two normalized 

puncture force parameters can be introduced, Fn4 and Fn5 in Equation 34 and 35,

FFnn4 = FFii

FFii

TTTT128BB �

eeUU

TTTT128BB

eeUU

MMMMMM MM MMMM� (34)

FFnn5 = FFii

FFii

TTTT128BB � (σ ffff eeUU)TTTT128BB

(σ ffff eeUU)MMMM MM MMMMMM� (35)

where tabulated results are shown in Table 28 and the two Fn4 and Fn5 average normalized 

puncture force results are plotted in Figure 73 (namely eeUU in Figure 73(a) and eeUUσff ffff in Figure 

73(b)). 

The dispersion of the normalized puncture force data has increased when comparing the results 

in Figure 73 to the original uncorrected data (Fn1 in Figure 64). This is especially true with the 

eeUU corrected data, Fn4 where the standard deviation has increased 5x from 0.22 to 1.12 (see Table 

28). In the case of the eeUUσff ffff correction, Fn5, the standard deviation has increased less, namely 

2x from 0.22 to 0.47. However, the observed average normalized puncture force standard 

deviation using both of these correction methods is greater than observed with either of the 

strength corrections.

In summary, the strength corrections indicate the critical role that material strength plays in 

governing puncture force. Clearly, the ultimate strength of the material is the primary variable, 

although as shown yield strength also plays a role in collapsing the force-deflection curves of the 

full-scale puncture simulations. The other two stress-strain parameters examined, namely eeUU 

and eeUUσff ffff do not by themselves further collapse the puncture force data. Although this 

approach is useful for identifying the most critical variable, the cross-coupling (or in effect the 

interaction) that may occur with the different stress-strain parameters can only be established by 

using all of the different parameters in different forms of a model to relate stress-strain 

parameters to puncture energy.
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(a) elongation (at ultimate) correction

(b) area under the stress-strain curve (to ultimate) correction

Figure 73. Relative puncture force after two different corrections including ductility.
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3.7 Puncture Energy Models

The above observations on the role stress-strain curve parameters allow us to put together a 

strength model that governs the material effects on the tank puncture energy. Remember that the 

puncture energy is obtained by integrating the force deflection curve up to the point of puncture. 

As shown in Figure 72, yield strength scaling does a reasonable job of collapsing the forcedeflection curves for materials of varied strengths. Similarly, the force magnitude at which the 

tank is punctured is primarily controlled by the material ultimate strength. Although the two 

strength parameters correlate the different types of data reasonably well, it is arguable whether 

they provide a full correlation since the third significant parameter governing the stress-strain 

curve, elongation, is absent. Note that in Figure 72, the material with the highest ductility (304L 

stainless steel) has the largest variation in the functional model formulation. Therefore, 

elongation will also be considered as a variable in the puncture energy modeling. It will be 

included in two ways; first as a stand-alone term and second in a formulation using the energy 

under the stress-strain curve.

3.7.1 Model Form and Calibration

When developing a model, the first step is to understand what parameters govern behavior. This 

was accomplished to some degree in the previous Section 3.6.2 of this report where different 

stress-strain parameters were examined in the context of the puncture force. The next step is to 

use the governing physics to postulate a form of the model (coefficients and powers and 

combined terms including different parameters). Unfortunately, the puncture process is too 

complex to understand and capture the underlying physics with any degree of certainty. Recall, 

all of the puncture energy results were obtained from full-scale structural analyses (finite element 

analyses) that are not readily governed by simple relationships that allow understanding the role 

of the different variables involved. The tank deformation process includes contributions from 

the inertial behavior and kinematics of the tank, local deformation response in the dent formation 

(e.g. moving plastic hinges), and internal pressure work. Generating the average puncture 

energy values for each material is a complex, time-consuming undertaking utilizing all of the 

variables involved in a structural analysis.

Therefore, the approach utilized herein is to attempt to correlate puncture energy with stressstrain parameters using the simplest, lowest power correlations while minimizing interaction 

effects where multiple variables are combined in terms. If the simplest models manage to 

correlate the available data, there is no need for a more complex higher order model. Three 

models are utilized herein: one using two parameters (ultimate and yield strength) and two using 

three parameters (ultimate strength, yield strength and elongation at ultimate). We used the 

averaged normalized puncture energy values (En1 as shown in Figure 65) obtained from the set of 
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side impact calculations to correlate the models and obtain regression constants. The definitions 

of the three models are as follows:

EEFF = AA1σσUU + AA2σσYY (36)

EEFF = BB1σσUU + BB2σσYY + BB3eeUU (37)

EEFF = CC1σσUU + CC2σσYY + CC3eeUUσσ ffff = CC1σσUU + CC2σσYY + CC3eeUU(σσUU + σσYY)/2 (38)

where Efit (the curve fit normalized energy from the model) corresponds to the En1 values for the 

different materials and the constants An, Bn and Cn were determined from linear regression of the 

normalized energy and the different model parameters (σσUU, σYY and eeUU). To aid in this companion 

discussion, the shorthand description of the three models in Equations 36-38 are the U-Y, U-Y-e 

and U-Y-eFlow models, respectively.

A summary of the models and the regression constants is provided in Table 29. The form of the 

model is shown along with the parameters involved, which include the curve fit constant (An, Bn

and Cn) and the parameters that characterize the stress-strain curve. The measure of “goodness 

of fit”, the R2 error result (last column of Table 29) also provides a relative sense of the error 

incurred in the regression. What is interesting is that these three different models all tend to fit 

the calibration data reasonably well (exhibiting R2 error results in excess of 0.9). The similarity 

of the R2 error results for the three fits is striking; all yield values in the range of 0.92-0.93.

Table 29. Curve fit parameters for the two different models.

Model Name

Parameters Used

Form of Equation Eqn.

No.

Regression

Constants

Fit R2

σUU error

(ksi)

σYY

(ksi)

Elong at 

UTS, in/in

U-Y   AA1σσUU + AA2σσYY (36)

A1 = 0.0200

A2 = -0.0113

0.913

U-Y-e    BB1σσUU + BB2σσYY + BB3eeUU (37)

B1 = 0.0140

B2 = -0.0054

B3 = 0.821

0.917

U-Y-eFlow    CC1σσUU + CC2σσYY + CC3eeUUσσ ffff (38)

C1 = 0.0132

C2 = -0.0052

C3 = 0.0146

0.926

Further detail of the fits, and the calibration data used to perform the regressions, are indicated in 

Table 30 along with the corresponding Efit results from each of the models and the percent errors 

resulting at each observation. As shown, average normalized (to TC128B) puncture energy 
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results for seven materials were used to derive the regression constants. The similarity of the 

three fits was previously indicated with similar R2 error results in Table 29. This similarity is 

also apparent from the statistical error analysis in Table 30. In terms of average error, the two 

three parameter models (eqns. 37 and 38) outperform the two parameter model (eqn 36) with 

average error for U-Y-eFlow 65% of that observed with the two parameter U-Y model. Standard 

deviations of error for all three are quite similar, in the range of 6.8-7.1%. Similarly the 

maximum and minimum error values observed are also fairly similar for the three fits.

The overall performance of the regression models relative to the calibration data is further 

examined in Figure 74 where the predicted results are plotted against the calibration data. The 

solid line would indicate perfect agreement between the calibration data and the fit data. All 

three models indicate good agreement with the calibration data with the predicted normalized 

energy resulting from the models typically within the dashed lines representing ±10% of the 

calibration data. This result is consistent with the findings in Table 30 with the standard 

deviation of the error; using the typical ±2 standard deviation comparison would imply 

prediction of the calibration data within 13.6-14.2% (the 95% confidence interval assuming a 

normal distribution of error).

Figure 74. Curve fit comparisons and results for the three different models (data shown used to 

derive curve fit parameters).
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Table 30. Curve fit results for the three different models.

Material

Normalized

σσUU

ksi

σσYY

ksi

Elong Specific Curve Fit Model Utilized [equation no.]

Average at UTS U-Y [36] U-Y-e [37] U-Y-eFlow [38]

Energy eeUU, in/in Efit %error Efit %error Efit %error

A516-70 0.84 72 48 0.18 0.90 6.5 0.90 6.4 0.86 2.2

HY80 0.89 96 84 0.12 0.97 9.0 0.99 11.1 0.99 11.4

TC128B 1.00 84 58 0.16 1.03 2.8 0.99 -0.35 0.98 -2.1

HY100 1.03 114 102 0.09 1.13 10.3 1.12 9.4 1.12 9.6

A709 1.25 121 108 0.09 1.20 -3.4 1.19 -4.6 1.19 -4.1

HY130 1.39 141 136 0.07 1.29 -7.6 1.30 -6.6 1.31 -6.3

SS304L 1.56 98 41 0.44 1.50 -3.5 1.51 -2.6 1.53 -1.4

average: 2.02 1.8 1.3

standard deviation: 6.96 7.1 6.8

minimum: -7.61 -6.6 -6.3

maximum: 10.26 11.1 11.4

In general, the results of all three models are fairly consistent and similar in magnitude across the 

range of energy levels considered. Prediction errors are mixed between the three models with no 

clear systematic trend exhibited as normalized puncture energy increases. What is striking about 

the three different formulations is that the predicted results are fairly consistent and the R2 error 

is so similar between the three. Although the reason for this is unknown, it could simply be a 

consequence of the predominant role of the most critical tensile strength parameter. This 

parameter could be controlling the overall behavior with only a secondary influence from the 

other parameters included in the different formulations. 

However, on balance it is valuable to have all three models. Inevitably, the models will be used 

to extrapolate to materials outside those used to calibrate the model. In this case, it is unknown 

how each behaves in regimes outside the bound of the calibration. Therefore, by using all three 

models the widest range of potential behavior could be postulated with results from all three 

factored into any decisions regarding candidate materials and where resources should be invested 

in to gain performance improvements with different materials. 
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3.7.2 Model Sensitivity to Input Stress-Strain Parameters

The models themselves, and the coefficients developed for each, can provide some insight into 

how tensile property changes affect puncture energy. However, the intermingling of all three 

stress-strain characterizations in the third term of the U-Y-eFlow model does complicate this 

assessment. Moreover the quantities used to characterize stress-strain behavior are also related 

to one another. For instance, it is typical to see ductility loss as strength is increased. Moreover, 

ultimate and yield strength changes are typically in the same direction for both quantities. 

Nevertheless, further insight into the models can be gained by examining theoretical changes in 

the input parameters.

The sign of the coefficients of the different models detailed in Table 29 provides some insight 

into the sensitivity of the different variables involved in the fit. Not surprisingly, the ultimate 

strength coefficient is positive, indicating energy increases with an increase in strength. This is 

contrasted by a negative coefficient for yield strength in all three models; this implies that a 

concomitant increase in yield strength results in a decrease in puncture energy. Although at first 

blush this result may seem counterintuitive, it occurs due to the increased stiffness of the forcedeflection curve. Although the higher curve would dissipate more energy up to a given 

displacement, this effect is offset by the fact that the puncture strength is reached at lower 

displacement levels. This reduction in displacement at puncture produces the reduction in the 

puncture energy for higher yield stresses. Finally, an increase in elongation (at ultimate stress) 

results in an energy increase (see B3 coefficient in Equation 37).

The form of the different puncture models can also be used to provide a sense of the puncture 

energy change given a certain magnitude increase in the controlling parameters. This assessment 

is provided in Table 31 detailing the theoretical energy change (assuming an overall energy of 

unity) given perturbations in the input parameters. Keep in mind the changes detailed in Table 

31 differ. For instance, a strength change of ±5 ksi is a modest amount (within the scatter of testto-test variability). For most of the materials considered the 5 ksi increment is less than 10% of 

the baseline strength (yield or ultimate). On the other hand, a ductility change of 2% (0.02 in/in) 

is a larger change, especially given the effective range of eeUU material data (7-18% in Table 30, 

with the exception of the higher 44% for the stainless steel material).
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Table 31. Puncture energy change resulting from different stress-strain parameter changes.

Parameter

Change

Percent Change in Puncture Energy

U-Y model U-Y-E model U-Y-eFlow model

+5 ksi increase in σσUU +10.0 +7.01 +6.63

+5 ksi increase in σYY –5.66 –2.70 –2.59

0.02 in/in (2%) increase in eeUU n/a +1.64 +0.03

+5 ksi increase in both σσUU and σYY +4.37 +4.32 +4.04

+5 ksi increase in σσUU and -5 ksi 

decrease in σYY

+15.69 +9.71 +9.22

Based on the data in Table 31, the largest percent change in puncture energy, 7-10% overall, 

occurs with a +5 ksi increase in ultimate strength. A similar increase in yield strength results in a 

3-6% decrease in energy (consistent with the negative sign of the second term of all the models). 

A 0.02 in/in (change in elongation by 2%) results in a smaller change in energy, on the order of 

1.5%. Finally, Table 31 also indicates the puncture energy change for a like increase in both 

ultimate and yield, and a changing increase in ultimate (increasing) and yield (decreasing). The 

largest overall energy change, 9-16%, occurs for an increase in ultimate strength and a decrease 

in yield strength. 

3.7.3 Applying the Puncture Models to Different Materials

Additional material test data (summarized in Appendix A) is available from this program as well 

as previous tank car research programs that can be used with the models developed herein to 

determine the resulting effect on tank car puncture. Available tensile properties include several 

nominal-chemistry TC128B (from the NGRTC program), different chemical variants of TC128B 

(including medium- and low-sulfur TC128B tested during Phase II of this program as well as 

special TC128B data provided by Arcelor Mittal) and the NUCU and A514B data tested during 

Phase I of this program. These data, and the model predictions for normalized puncture energy, 

are summarized in Table 32 and Figure 75.

Predicted puncture energy for four datasets of nominal chemistry TC128B are shown to the left 

in Figure 75, including “3074” which is the calibration data used to derive the curve fit 

parameters. The average normalized puncture energy (predicted by the U-Y model) for these 

four nominal chemistry TC128B materials is shown by the red line with ±2 standard deviations 

also indicated. The ±2 standard deviation band corresponds to approximately ±10%. Hence the 
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lot-to-lot variability of nominal chemistry TC128B yields approximately the same error band as

we noted earlier during the model calibration shown in Figure 74.

The additional four TC128B datasets, with perturbed chemistries (three with reduced sulfur and 

one special chemistry variant), yield normalized puncture energy that is within the error band 

noted with different lots of TC128B material. This suggests that these modified chemistries do 

not yield markedly better puncture resistance than already observed in existing TC128B material 

(given the nominal TC128B band indicated in Figure 75). In fact, as sulfur decreases, the 

predicted puncture energy also decreases, regardless of which of the three puncture prediction 

models is utilized. This is likely a consequence of the lowered strength that is observed in lower 

sulfur material (without a concomitant increase in ductility).

The non-TC128B material shown in Table 32 and Figure 75 (NUCU and A514B, tested in this 

program) exhibit some enhancement of performance relative to TC128B. Both materials 

indicate puncture performance in the higher end of the TC128B range of behavior, although not 

significantly outside the range and therefore arguable from a statistical viewpoint. Of the two 

materials, the largest enhancement in puncture performances appears to be with A514B where all 

three models predict an increase in puncture performance. This is contrasted to the NUCU 

material where higher puncture energy is indicated by the U-Y model as opposed to the other 

two models that include a ductility term. 

Table 32. Predicted puncture energy for different variants of TC128B and other materials.

Material Type and Reference σ-ε Curve Model Result, Efit

σσUU σσYY eeUU U-Y U-Y-e U-Y-eFlow

Material Source Description ksi ksi in/in Eqn. 

(36)

Eqn. 

(37) Eqn. (38)

TC128B NGRTC-Dow TC ID. 3069 85 53 0.16 1.104 1.037 1.013

(nominal) NGRTC-Dow TC ID. 3074 84 58 0.16 1.027 0.996 0.979

NGRTC-Dow 0.777 plate 95 68 0.14 1.134 1.080 1.073

Phase I 0.750 plate 96 77 0.14 1.052 1.046 1.050

TC128B Phase II A-matl (med 0.005 S) 94 69 0.15 1.103 1.069 1.067

(varied S) Phase II S-matl (low 0.002 S) 93 69 0.14 1.083 1.047 1.041

Phase II T-matl (low 0.002 S) 86 65 0.16 0.988 0.987 0.980

TC128B(S) Arcellor Mittal special chemistry 83 53 0.14 1.059 0.992 0.964

NUCU Phase I A710-GrB 94 61 0.13 1.193 1.096 1.077

A514B Phase I A514-GrB 122 113 0.07 1.166 1.159 1.151

Shaded row is data used in model calibration
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Figure 75. Model results for different variants of TC128B and other materials.

The sensitivity analyses performed in Section 3.7.3 suggest the possibility, with the optimum 

range of stress-strain parameters, of energy improvements of 2.2-2.6x when compared to 

nominal TC128B material. However, it must be noted that this is for an optimum (e.g. not real) 

material. In examining the real materials examined herein, the largest puncture energy 

improvement observed was on the order of 1.3-1.5x for HY130 and 304L stainless steel. This 

puncture energy increase translates into a 15-20% increase in “allowable” impact speed before 

puncture occurs (see Figure 66). Even in the best case situation of a 2x puncture energy 

improvement, this translates into a 40% increase in impact speed before puncture occurs (again, 

see Figure 66). 

Given this, it is not unreasonable to note that the new and improved materials will net at best a 

modest improvement in puncture performance. Therefore higher levels of puncture 

improvement will likely be gained through additional modifications of the tank car structure that 

further improve puncture performance of tank cars.
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The three models in the previous section, derived by empirically fitting energy results from the 

structural modeling using different stress-strain parameters, provide a viable method to compare 

and contrast different candidate materials for tank car structure. Admittedly the ability of the 

models to predict behavior outside of the data used to calibrate the models is as yet unknown. 

Nevertheless, having a tool to rapidly screen candidate materials is beneficial. Without this tool, 

expensive and time-consuming laboratory tests and full-scale simulations would be required to 

evaluate different candidate materials. Moreover these models can be used to help the industry 

determine the possible impact of different material modifications that impact mechanical 

properties. Given these tools, puncture enhancement of different candidate materials can be 

predicted to aid in material selection decisions and cost-benefit analyses. 
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4 Summary and Conclusions

This report describes the results of a research program to characterize and evaluate tank car 

steels with the objective of improving railroad tank car tank integrity. In this work, puncture 

force/energy is evaluated for a range of materials and impact scenarios. Puncture behavior is a 

structural response not easily quantified in any closed form manner (hence puncture prediction 

requires full-scale numerical simulation to assess behavior). 

When this program was originally conceived, a number of different material failure models were 

proposed including the Bao-Wierzbicki, Gurson-Tvergaard and a maximum strain approach. 

These models involve different failure criteria that lead to development of puncture. In the end, 

the only suitable model was found to be the Bao-Wierzbicki model and hence it was focused on 

in this report.

The research program included detailed characterizations of various steel material samples 

(including a number of different TC128B variants). These detailed material characterizations 

included assessing tensile stress-strain properties as well as mechanical behavior of notched 

samples. As part of the research, detailed constitutive and damage models were developed for 

each material and the models were used to simulate the corresponding tests. An unexpected 

result of this process was that the commonly used von Mises yield criterion could not adequately 

model the full range of tests in the material characterization data. Specifically, the von Mises

assumption that the yield condition is independent of the mean stress resulted in the inability of 

the model to reproduce the load displacement curves for both the smooth and notched tensile 

tests. This effect was more pronounced in specific materials (i.e., the tank car 3069 and new 

TC128B steel from the NGRTC program). 

A summary of the material properties and material constitutive parameters is provided in Table 

A1 in Appendix A. The table includes the yield stress, ultimate stress, yield to ultimate (Y-U) 

ratio, elongation at ultimate stress, total elongation, smooth tensile to notched tensile ultimate 

ratio, Drucker Prager coefficient, modified Bao-Wierzbicki coefficient, longitudinal and 

transverse Charpy v-notch impact energy, whether the material has significant anisotropy in the 

longitudinal and transverse directions, and sulfur content for the materials (when available). 

In addition to the direct material characterization, a series of puncture analyses were performed 

for various candidate materials to identify the material characteristics that most strongly control 

puncture resistance. To assist in this evaluation, we intentionally selected candidate materials 

with a wide range of mechanical properties, as shown in Figure 74. These materials were used in 

a suite of puncture analyses under various side impact conditions using a chlorine tank car 

geometry. 
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The material properties were investigated in different combinations in an attempt to understand 

the material characteristics that contribute most significantly to the puncture resistance. The goal 

was to relate puncture behavior (as determined from the full-scale numerical simulations) to the 

stress-strain properties of the materials (strength and ductility). Three models are proposed in 

this work, as described in Equations 36, 37 and 38 with overall performance of the three depicted 

in Figure 74, that include linear combinations of ultimate strength, yield strength and ductility (in 

this case, the percent elongation at ultimate or the area under the stress-strain curve to the 

ultimate strength of the material). All three models provide excellent predictions of the observed 

puncture behavior (within 10% of the TC128B-normalized puncture energy). It is not possible to 

differentiate between the three models given the calibration data used herein; therefore, all three 

models are proposed since it is likely that candidate tank car materials will perturb the input 

variables beyond the calibration range involved herein (in essence, extrapolating the models 

beyond the range of calibration). 

The form of the models (in other words, how the different input parameters are combined) are 

simple linear combinations of different strength and ductility terms. This form is not based on 

any physics of the failure process; rather, the form is the simplest form available that provides a 

reasonable prediction of the numerical puncture simulations. The proposed models were 

determined empirically by least square fitting of the puncture data when combined with the 

different input variables.

Although these models are purely empirical, an examination of the numerical puncture force 

response clearly indicates the compelling role of the ultimate strength of the material in 

predicting puncture behavior. However, the force-deflection characteristics of the simulations 

exhibit reasonable correlation to the yield strength of the material. An increase in ultimate 

strength leads to higher puncture energy; conversely, an increase in yield strength leads to a 

lower puncture energy4

. Nevertheless the utility of a puncture model including only strength 

(ultimate and yield) variables is limited since it does not adequately capture the effect of 

differing levels of ductility in the failure process (hence the introduction of the models that 

capture ductility).

These models provide a basis to predict the effect of differing strength and ductility on the 

puncture behavior of a rail tank car. However, material selection is not simply based upon 

stress-strain curve properties. There are other issues involved (such as weldability, corrosion and 

fatigue resistance, toughness, material cost etc.) that clearly are not captured by these models. 

Nevertheless, the three material puncture models provide a viable method to compare and 

 4 Subsequent to the publication of the initial draft of this report, additional analyses were performed for head impacts 

of different materials (see Reference 51). These analyses found similar trends for the effects of yield and ultimate 

strength but with higher magnitudes of the effects. 
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contrast different candidate materials for tank car structure. Admittedly the ability of the models 

to predict behavior outside of the data used to calibrate the models is as yet unknown. 

A predictive tool to rapidly screen candidate materials is beneficial to the tank car industry. 

Without this tool, expensive and time-consuming laboratory tests and full-scale simulations 

would be required to evaluate different candidate materials. Moreover these models can be used 

to help the industry determine the possible impact of different material modifications that impact 

mechanical properties. Given these tools, puncture enhancement of different candidate materials 

can be predicted to aid in material selection decisions and cost-benefit analyses. Applying these 

models to various combinations of strength and ductility indicates that the new and improved 

materials will net at best a modest improvement in puncture performance.

The current requirements for TC128B specify a minimum value of the yield stress and both a 

minimum and maximum value of the ultimate strength. However, it is likely that these 

specifications are provided more reflecting the chemistry of the TC128B rather than overall 

design considerations. It is likely that the minimum values are required to ensure that the tank 

car design has sufficient integrity for the operating conditions. However, considering only 

puncture resistance, there is no reason to specify a limit on the maximum ultimate strength for 

the material. As the puncture models indicate, from a puncture viewpoint it might make sense to 

place a limit on the maximum allowable yield stress for the material. But material specifications 

are a complex combination of characteristics of both the material and the design considerations.

In addition to identifying the characteristic of the materials that should be further investigated, 

there is some additional work that should be performed to carry this model further. Primarily, 

the strength model was shown to work well for side impacts on a chlorine tank car design. Some 

additional work is needed to confirm if the same (or similar) results are obtained for head 

impacts and on other tank designs of different thicknesses and at different pressure levels. 
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5 References

1. Kirkpatrick, S.W., “Detailed Puncture Analyses of Various Tank Car Designs,” ARA Final 

Technical Report, Prepared for the Next Generation Railroad Tank Car (NGRTC) Project, 

January, 2009.

2. McKeighan, P.C., “Tensile Properties and Stress-Strain Behavior of Various Steel Products

Used in Fabricating Test Specimen for the NGRTC Program,” NGRTC Project 

Memorandum, Southwest Research Institute, 21 November 2007. 

3. McKeighan, P.C., “Notched Tensile Properties of Tank Car Material from Full Scale Test 

No. 1 (Car No. 3069) and Test No. 2 (3074) Oriented in the Transverse Direction,” NGRTC 

Project Memorandum, Southwest Research Institute, 20 November 2007. 

4. McKeighan, P.C., “Notched Tensile Properties of Thickest TC128B Tank Car Material from 

Material Inventory for Fabricating Test Specimens,” NGRTC Project Memorandum, 

Southwest Research Institute, 6 December 2007. 

5. McKeighan, P.C., “Shear Tests on TC128B Normalized Material of Two Different 

Thicknesses,” NGRTC Project Memorandum, Southwest Research Institute, December 2007. 

6. McKeighan, P.C., “Puncture Tests on Jacket Material (A1011, 90X) and Normalized 

TC128B Shell Material (two thicknesses)- Revised,” NGRTC Project Memorandum, 

Southwest Research Institute, 17 December 2007. 

7. McKeighan, P.C., “Puncture Behavior of 0.48-inch Thick A516 Material,” NGRTC Project 

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the Gurson Model,” LS-DYNA Anwenderforum, Ulm, 2006. 

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Appendix A – Supplemental Data

Table A1. Comparison of the various candidate tank car material properties.

Figure A1. Tensile stress-strain results of special TC128B (data provided by ArcelorMittal)5

 5

 Special (reduced carbon and niobium) TC128B material produced by ArcelorMittal (data supplied by William 

Heitmann), reference De, A.K., Gungor, O.E. and Manohar, M., “Development of a High Toughness Steel with 

Enhanced Upper Shelf Energy for Pressure Tank Car Applications,” ArcelorMittal Global R&D, presentation at the 

Tank Car Committee Meeting, Dallas, TX, April 2015.

Material

Yield 

Stress 

(ksi)

Ultimate 

Stress 

(ksi)

Y-U

ratio

Elong. 

At UTS Elong. ST/NTRatio

D-P 

Coeff.

(α)

Mod. BW 

Coeff.

(n)

Long. 

CVN 

(ft-lbs)

Trans. 

CVN 

(ft-lbs)

L-T

Isotropy Sulfur

TC128B (3069) 53 85 1.60 0.16 0.32 1.47 0.120 1.6 146 80 Yes -

TC128B (3074) 58 84 1.44 0.16 0.32 1.50 0.050 1.0 136 106 Low 0.003

TC128B (0.777) 68 95 1.40 0.14 0.32 1.42 0.195 1.0 - - Low 0.007

TC128B (0.750) 77 96 1.25 0.14 0.29 1.58 0.040 1.0 70 65 Low 0.008

TC128B (A289) 69 94 1.36 0.15 0.29 1.54 0.050 1.0 120 105 Low 0.005

TC128B (S288) 69 93 1.35 0.14 0.28 1.53 0.050 1.6 117 119 Low 0.002

TC128B (T290) 65 86 1.31 0.16 0.33 1.53 0.050 TBD 130 147 Low 0.002

NUCU (A710-B) 61 94 1.54 0.13 0.25 1.53 0.015 1.0 139 175 Low -

A514B 113 122 1.08 0.07 0.18 1.61 0.035 2.2 96 139 Yes -

HPS100W 108 121 1.12 0.09 0.25 1.61 0.045 1.6 180 205 Low -

HY-80 84 96 1.14 0.12 0.26 - - - - - -

HY-100 102 114 1.12 0.09 0.23 - - - - - -

HY-130 136 141 1.04 0.07 0.23 1.65 - 1.9 - - - -

SS 304L 41 98.0 2.40 0.44 0.55 - - - - - -

A516-70 48 72 1.50 0.18 0.40 - - - - - -

 

Strain, in/in

0.0 0.1 0.2 0.3 0.4

Stress, ksi

0

10

20

30

40

50

60

70

80

90 151N3SR3_L1

151N3SR3_L2

Strain, in/in

0.000 0.001 0.002 0.003 0.004 0.005 Stress, ksi

0

10

20

30

40

50

60

Spec. ID No. UTS, ksi YS, ksi elong, %

151N3SR3_L1 82.3 52.5 41.5

151N3SR3_L2 83.0 53.2 40.6

average: 82.7 52.9 41.1
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Appendix B – Characterization of 304L Stainless Steel

Introduction

During the performance of the TWP-10 project, described in the main body of this report, the 

steel characteristics required for improved puncture resistance were identified. The 

recommendations coming out of that TWP-10 research effort included:

1. Investigate high strength (130 ksi) steels but with lower yield and properties desirable for 

tank car steels.

2. Perform a detailed characterization of 304L stainless steel.

3. Investigate lower cost alternatives that provide properties similar to 304L stainless.

The second recommendation was selected as a priority and the ATCCRP committee funded a 

follow-on effort to complete this task. The results of this subsequent effort are described in this 

appendix. 

The statement of work for the follow-on effort included:

Task 1 – Perform a TWP-10 material characterization test series on ASTM A240 Type 304L

stainless steel including tensile, notched tensile, and high-rate tensile test series. 

Task 2 – Develop detailed TWP-10 constitutive model including a Drucker-Prager yield 

criterion and Bao-Wierzbicki damage and failure model. 

Task 3 – Confirm material performance in impact calculations.

Characterization Testing

The material characterization test program included longitudinal and transverse tensile tests, 

notched round bar tensile tests, and longitudinal tensile tests at elevated strain rates. The 

objective was to perform three repeat tests at each condition to assess repeatability of results. 

The tensile and notched tensile data for the 304L stainless material are shown in Figure B1. 

Similarly, the high rate tensile testing results are shown in Figure B2. These high rate tests use a 

round bar specimen geometry with a shortened specimen gauge length. For comparison, the 

quasistatic longitudinal tensile behavior measured with the standard round bar tensile test with 

the 2-inch gauge section length is also provided in the figure. 
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(a) Tensile data summary

(b) Notched tensile data only

Figure B1. Summary of the 304L stainless quasistatic tensile test data.
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Figure B2. Summary of the 304L stainless tensile test data at elevated strain rates.

The tensile data, shown in Figure B1, has a yield strength of 36 ksi and an ultimate tensile 

strength of 90 ksi with an elongation of approximately 0.68. These values compare favorably to 

the required ASME A240 minimum properties for 304L stainless steel of 25 ksi yield strength, 

70 ksi tensile strength, and 40% elongation. It is also reasonably consistent with other data 

found in open literature for 304L stainless steel. In addition the data compares favorably to that 

used to create the ASTM A240 304L used in the original TWP-10 study described in Section 3.5. 

The primary difference is approximately a 5 ksi lower tensile strength of the new data. 

The notched tensile data, shown in Figure B1, indicates a different behavior from the previous 

steels tested in that the notched specimens are more different from the smooth round bar result 

and there is less variation between the different notch radii than seen for the previous carbon 

steels tested. We believe this is primarily a result of the stainless having both a very large 

ductility and a large amount of hardening that result in a modification of the notch shape and 

corresponding influence on the triaxiality levels in the notched specimens as they deform. Note 

that there was also a slightly different specimen geometry used for these notched tensile tests in 

this series compared to the original specimen design. The original design used in the baseline 

TWP-10 test series, shown in Figure B3, uses a 0.50-inch bar diameter outside the notch. The 

new design used in this TWP-10A test series, shown in Figure B4, used a 0.38-inch bar diameter 

outside the notch. Analysis of the two specimen geometries shows that this bar diameter plays a 
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role in the measured response, but is not the primary factor influencing the characteristics of the 

notched tensile test behaviors. 

Figure B3. Notched specimen geometry used in previous testing detailed in the body of this 

report.

Figure B4. Notched specimen geometry used in stainless steel testing detailed in this Appendix.

The high strain rate tensile data, shown in Figure B2, shows a more significant strain rate effect 

than typically seen for carbon steels in the range of rates tested. The ultimate strength of the 

material increases by approximately 7% over the range of rates tested and the elongation is 

reduced by approximately 15%. At intermediate strain levels, the rate effects on the stress can be 

more significant (approximately 10-15%). However, due to the strain rates and distribution of 

plastic strain magnitudes seen in the tank impact behavior, we believe that accurate assessments 

of the impact response will still be obtained in simulations that neglect the strain rate effects. 
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The conversion of the smooth round bar tensile test data to true stress and the corresponding 

piecewise linear fit to the data used for the material constitutive model are both shown in Figure 

B5. This conversion to the true stress-strain behaviors was described in Section 2.4 of this 

report. This constitutive model fit was used to simulate the tensile test configuration and the 

corresponding comparison to the test data is shown in Figure B6. The good agreement between 

the tests and model show that the tabular fit is accurate and has been correctly implemented in 

the model. 

Figure B5. Comparison of the measured and calculated 304L stainless tensile behavior.

The resulting constitutive model developed from the smooth round bar tensile test was 

subsequently applied to simulate the notched round bar tensile specimens. The correlation of the 

measured and calculated behaviors for the notched tensile tests is shown in Figure B7. The 

model gives good agreement for both the smooth round bar tensile test and for the notched 

tensile test with the smallest 0.05-inch notch radius. For the intermediate 0.10-inch and 0.25-

inch notch radii, the model under-predicts the peak tensile strength (by approximately 3% and 

6% respectively) and elongation. The problem is that any changes that could be made to the 

model to improve correlation at these intermediate notch radii would reduce the correlation at 

either (or both) of the smooth tensile or sharp notch radii test conditions. As a result, this model 

was used as the final fit to the data and the corresponding model parameters are provided in 

Table B1.
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Figure B6. Comparison of the measured and calculated 304L stainless tensile behavior.

Figure B7. Comparison of the measured and calculated 304L stainless tensile behavior.
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Table B1. Material constitutive parameters and tabular 304L stress-strain values.

Material Constitutive Parameters

Bao Wierzbicki Coefficient - A 0.96

Bao Wierzbicki Coefficient - B 2.40

Modified Bao Wierzbicki Coefficient - n 1.00

Drucker Prager Coefficient - α 0.00

Point No. Plastic Strain (in/in) True Stress (ksi)

1 0.000E+00 36.0

2 2.483E-03 42.5

3 1.233E-02 50.0

4 4.098E-02 60.5

5 9.745E-02 76.5

6 1.967E-01 99.3

7 2.961E-01 117.6

8 3.955E-01 134.6

9 4.945E-01 149.0

10 5.900E-01 159.5

11 6.900E-01 167.5

12 1.690E+00 235.0

The resulting constitutive model was applied to the simulation of blunt impact tank punctures. 

The initial impact scenario investigated was an impact of a 105J600I tank car design with a 6x6-

inch impactor. For the initial investigation, three different simulations were compared. One of 

the simulations was the original simulation performed with the ASTM A240 304 stainless steel 

as part of the original TWP-10 study described in Section 3.5. Since that time, some additional 

improvements were made to the puncture models and modeling parameters. In addition, the

version of LS-DYNA currently being used for analyses has been updated. As a result the second 

simulation was performed using an updated impact model but with the original ASTM A240 304
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stainless steel constitutive model. Finally, a simulation was performed using the new ASTM 

A240 304L stainless steel constitutive model described in this appendix. 

The comparison of the calculated force-deflection characteristics for the three impact simulations 

is shown in Figure B8. The first observation is that the two new simulations, using the original 

and the new 304L stainless steel constitutive models, are nearly identical. This is good news in 

that it indicates the new model does not significantly influence the puncture behavior compared 

to the original model used in the study. The outlier is the original impact simulation that

corresponds well for the majority of the force-deflection curve but punctures prematurely at a 

force that is approximately 8% lower than in the new simulations. Because of the kinematics of 

this impact scenario, this premature puncture resulted in a significant 36 percent reduction in the 

calculated puncture energy, compared to the new simulations. 

Figure B8. Comparison of the calculated stainless steel tank impact behaviors.

An investigation determined that a time-step based element erosion parameter (DTMIN) was 

responsible for the premature failure in the old simulation. This parameter is set to allow for 

elements that experience a large deformation to be deleted if they are controlling the calculation 

timestep at a level below the fraction of the original timestep. The idea is to prevent a few 

elements that have been highly distorted from significantly reducing the calculation time step 

size, and consequently increasing the calculation run time. Typically, these are elements along a 
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fracture zone or in a high distortion crush zone and deleting them has no significant influence on 

the calculated response. 

In this simulation, the high ductility of the stainless steel, combined with the assigned value of 

DTMIN, resulted in element deletions that did influence the response for this scenario. 

Additional analyses were therefore performed to assess the magnitude of the effect. The 

additional calculations were performed for the 3-inch, 9-inch, and 12-inch impactors using the 

new constitutive model and updated impact models. The comparisons of the original and 

updated model simulations are shown in Figure B9. The comparison shows that the effect seen 

in the 6-inch impactor is by far the largest for the various impact conditions. The other impact 

conditions see a smaller single digit difference in both puncture force and puncture energy. As a 

result, the conclusions of the high puncture performance of 304L stainless steel in the previous 

analyses are still valid and the performance gain estimates are conservative based on these 

previous analyses. 

Figure B9. Comparison of the measured and calculated 304L stainless tensile behavior.

A secondary check on the modeling effect of DTMIN was also performed using updated 

analyses on the material with the second largest ductility (elongation) in the material screening

study. This was the A516-70 material described in Section 3.5. In these simulations the effects 

of the new modeling parameters was significantly less than seen in the 304L stainless steel. 

Thus, the effect of the modeling parameters on puncture response were primarily a result of the 
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unusually high elongation behavior of stainless steel and not significant for the other materials 

evaluated. 

Summary and Conclusions

During the performance of the main TWP-10 project, the steel characteristics required for 

significant increases in puncture resistance were identified. The recommendations coming out of 

that research effort included performing a detailed characterization of 304L stainless steel to 

provide test data and confirm the analyses predicting high puncture performance for that 

material.

The material characterization test program performed on the 304L stainless steel included 

longitudinal and transverse tensile tests, notched round bar tensile tests, and longitudinal tensile 

tests at elevated strain rates. Good quality data was obtained and the results were summarized in 

this appendix. 

A material constitutive and damage model was developed based on the new 304L stainless 

material characterization tests and the existing TWP-10 methodology. The model was used in 

tank impact analyses to re-evaluate the puncture performance of the 304L stainless steel. The 

assessment identified an inaccuracy introduced in the original analyses from a modeling 

parameter. However, the assessment determined that the effect was relatively small and would 

not have significantly changed the results or conclusions of the original study. Furthermore, the 

effect would have slightly underestimated the performance of the stainless steel material. 

The final conclusion is that the testing and analyses performed in this supplemental study are 

consistent with the previous results and continue to indicate the superior puncture resistance of 

the 304L stainless steel compared to the carbon steels evaluated. Further validation of this 

conclusion would require impact and puncture testing on a 304L stainless steel tank structure or 

an alternative impact and puncture test specimens.